Lesson OVERVIEW of the first group of lessons on arithmetic word problems

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<H2>OVERVIEW of the first group of lessons on arithmetic word problems</H2>

Below is the list of my lessons on arithmetic word problems in this site:

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-word-problems-to-solve-them-MENTALLY.lesson>Arithmetic word problems to solve them MENTALLY</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Solving-arithmetic-word-problems-by-reasoning.lesson>Solving arithmetic word problems by reasoning</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Simple-arithmetic-word-problems-solved-in-a-right-way.lesson>Simple arithmetic word problems solved in a right way</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-coin-problems.lesson>Arithmetic coin problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Simple-arithmetic-word-problems-on-rate-of-work.lesson>Simple arithmetic word problems on "rate of work" </A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Simple-and-simplest-arithmetic-Travel-and-Distanse-problems.lesson>Simple and simplest arithmetic Travel & Distance problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Typical-arithmetic-Travel-and-Distance-problems.lesson>Typical arithmetic Travel & Distance problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Entertaining-catching-up-arithmetic-Travel-and-Distance-problems.lesson>Entertaining catching up arithmetic Travel & Distance problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Other-basic-arithmetic-Travel-and-Distance-problems.lesson>Other basic arithmetic Travel & Distance problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-word-problems-on-Travel-and-Distance.lesson>Advanced arithmetic word problems on Travel & Distance</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Finding-travel-time-and-average-rate.lesson>Finding travel time and average rate</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Flying-back-and-forth.lesson>Flying back and forth</A>

<H3>List of lessons with short annotations</H3>

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-word-problems-to-solve-them-MENTALLY.lesson>Arithmetic word problems to solve them MENTALLY</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;There are a total of &nbsp;20 &nbsp;lions, &nbsp;tigers, &nbsp;and bears at the local zoo.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The number of tigers is &nbsp;2 &nbsp;more than the number of lions.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The number of bears is &nbsp;3 &nbsp;more than the number of lions.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How many lions are at the zoo?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;The sum of two numbers is &nbsp;92, &nbsp;their difference is &nbsp;20. &nbsp;&nbsp;Find the numbers.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;Gopal had twice as many &nbsp;50c coins as &nbsp;20c &nbsp;coins. &nbsp;He also had &nbsp;5 &nbsp;times as many &nbsp;10c &nbsp;coins as &nbsp;50c &nbsp;coins.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If he had &nbsp;$15.40, &nbsp;how many &nbsp;50c &nbsp;coins did he have?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;A deli is offering a special for its sandwiches. &nbsp;A customer will receive three free sandwiches

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for every five sandwiches purchased. &nbsp;Jane ordered &nbsp;101 &nbsp;sandwiches for an office party.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 5. &nbsp;Xavier works in an amusement park and is helping decorate it with strands of lights.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This morning, &nbsp;he used a total of &nbsp;28 &nbsp;strands of lights to decorate &nbsp;4 &nbsp;bushes and &nbsp;1 &nbsp;tree.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This afternoon, &nbsp;he strung lights on &nbsp;3 &nbsp;bushes and &nbsp;1 &nbsp;tree, &nbsp;using a total of &nbsp;24 &nbsp;strands of lights.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Assuming that all bushes are decorated one way and all trees are decorated another,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;how many strands did &nbsp;Xavier use on each bush and on each tree ?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 6. &nbsp;The glee club needs to raise money for the spring trip to &nbsp;Europe, &nbsp;so the members are assembling holiday wreaths to sell.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Before lunch, &nbsp;they assembled &nbsp;12 &nbsp;regular wreaths and &nbsp;20 &nbsp;deluxe wreaths, &nbsp;which used a total of &nbsp;168 &nbsp;pinecones.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;After lunch, &nbsp;they assembled &nbsp;12 &nbsp;regular wreaths and &nbsp;15 &nbsp;deluxe wreaths, &nbsp;using a total of &nbsp;138 &nbsp;pinecones.

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Solving-arithmetic-word-problems-by-reasoning.lesson>Solving arithmetic word problems by reasoning</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;An advertisement from the back of &nbsp;Denton checklist:

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(1)  &nbsp;&nbsp;$1300 sofa and love seat

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2)  &nbsp;&nbsp;$1400 sofa and two chairs

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(3)  &nbsp;&nbsp;$1600 sofa, &nbsp;love seat, &nbsp;one chair

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;Ben earns &nbsp;20 cents &nbsp;for every card he sells. &nbsp;When he sells a whole box of &nbsp;12 &nbsp;cards he earns an extra &nbsp;$2.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;The ratio of the number of blue sticks to the number of green sticks in a box was &nbsp;4:1.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;When &nbsp;David took out some blue and sticks and replaced them with an equal number of green sticks,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;the ratio of the number of blue sticks to the number of green sticks became &nbsp;3:1.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(a) &nbsp;&nbsp;find the total number of blue and green sticks in the box,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(b) &nbsp;&nbsp;find the number of green sticks in the box at first.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;Marty’s age is &nbsp;36, &nbsp;which is &nbsp;12 &nbsp;more than &nbsp;4 &nbsp;times &nbsp;Daisy’s age. &nbsp;How old is &nbsp;Daisy?

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Simple-arithmetic-word-problems-solved-in-a-right-way.lesson>Simple arithmetic word problems solved in a right way</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;If four loaves of bread costs &nbsp;$8,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and a loaf of bread, &nbsp;two bags of oranges and a basket of apples costs &nbsp;$17,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;If a patient takes &nbsp;1/2 &nbsp;teaspoon orally every &nbsp;8 hours,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;then for how many days a supply of &nbsp;60 mL of the medication will last ?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;Tobramycin &nbsp;Eye &nbsp;Suspension, &nbsp;1 drop into each eye &nbsp;3 &nbsp;times daily, &nbsp;10ml bottle.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;A soap manufacturer spent &nbsp;60000 &nbsp;rupees on radio, &nbsp;magazine and &nbsp;TV &nbsp;advertising.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If he spent as much on &nbsp;TV &nbsp;advertising as on magazines and radio together,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and spent on magazines and &nbsp;TV &nbsp;combined equals five times that spent on radio,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 5. &nbsp;Sarah has $5.25 worth of change in nickels and dimes.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If she has &nbsp;3 &nbsp;times as many nickels as dimes, &nbsp;how many of each type of coin does she have?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 6. &nbsp;A total of &nbsp;320 &nbsp;tickets were sold for the school play. &nbsp;They were either adult tickets or student tickets.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The number of student tickets sold was three times the number of adult tickets sold.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How many adult tickets were sold?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 7. &nbsp;A fish tank has a base area of &nbsp;4500 cm^2 &nbsp;and is filled with water to a depth of &nbsp;12 &nbsp;cm.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If the height of the tank is &nbsp;25 cm, &nbsp;how much more water is needed to fill the tank to the brim?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 8. &nbsp;A ﬁsh tank in a pet store was less than half full of water

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;when a worker turned on a hose to ﬁll the tank at a constant rate.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;After the hose was on for &nbsp;5 &nbsp;minutes, &nbsp;the tank was exactly half full.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;After the hose was on for &nbsp;30 &nbsp;minutes, &nbsp;the tank was three-quarters full.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How many minutes did it take after the hose was turned on for the tank to be completely ﬁlled with water?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 9. &nbsp;A man travels in one direction for &nbsp;8 &nbsp;hours at a rate of &nbsp;100 &nbsp;miles per hour,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and then returns back. &nbsp;If his average speed for the whole trip is &nbsp;80 &nbsp;miles per hour,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 10. &nbsp;A baker needs &nbsp;4 &nbsp;eggs to make a cake, and &nbsp;6 &nbsp;eggs to make a flan.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If the baker wants to make &nbsp;8 &nbsp;cakes and &nbsp;6 &nbsp;flans,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 11. &nbsp;An appliance store sells additional warranties on its refrigerators.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;twenty percent of the buyers buy the limited warranty for &nbsp;$100

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;What is the expected revenue for the store from the warranty if it sells &nbsp;120 &nbsp;refrigerators?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 12. &nbsp;A box with a square base and no top is to be made from a square piece of carboard

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;by cutting &nbsp;4 in. squares from each corner and folding up the sides.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The box is to hold &nbsp;17956 in3. &nbsp;How big a piece of cardboard is needed?

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-coin-problems.lesson>Arithmetic coin problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;A collection of coins has five nickels and &nbsp;7 &nbsp;dimes. &nbsp;Find the total value of the coins.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;Andrew has seven dimes and &nbsp;5 &nbsp;quarters. &nbsp;Find the total value of the coins.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;A collection of coins has several nickels and &nbsp;7 &nbsp;dimes.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The total value of the coins is &nbsp;95 &nbsp;cents. &nbsp;Find the number of nickels in the collection.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;Alisa has &nbsp;7 &nbsp;dimes and several quarters.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The total value of coins Alisa has is &nbsp;$1.45 &nbsp;cents. &nbsp;Find the number of quarters &nbsp;Alisa has.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 5. &nbsp;There are several nickels and equal number of dimes.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Altogether, &nbsp;they comprise &nbsp;$1.35. &nbsp;How many nickels are there? &nbsp;How many dimes?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 6. &nbsp;There are several dimes and equal number of quarters.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Altogether, they comprise &nbsp;$1.05. &nbsp;How many dimes are there? &nbsp;How many quarters?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 7. &nbsp;There are several nickels and three times as many dimes as nickels.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Altogether, &nbsp;they comprise &nbsp;$1.40. &nbsp;How many nickels are there? &nbsp;How many dimes?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 8. &nbsp;There are several nickels and three times as many quarters as nickels.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Altogether, &nbsp;they comprise &nbsp;$2.40. &nbsp;How many nickels are there? &nbsp;How many quarters?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 9. &nbsp;Roberta has &nbsp;4 &nbsp;dollars in dimes and quarters. &nbsp;She has &nbsp;5 more dimes than quarters.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In total, &nbsp;Roberta has &nbsp;25 &nbsp;coins. &nbsp;How many coins of each designation does Roberta have?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 10. &nbsp;There are several nickels and two more than three times as many quarters as nickels.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Altogether, &nbsp;they comprise &nbsp;$3.70. &nbsp;How many nickels are there? &nbsp;How many quarters?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 11. &nbsp;There are several dimes and three more than two times as many quarters as dimes.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Altogether, &nbsp;they comprise &nbsp;$4.35.&nbsp;How many dimes are there? &nbsp;How many quarters?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 12. &nbsp;Gopal had twice as many &nbsp;50c coins as &nbsp;20c coins. &nbsp;He also had &nbsp;5 &nbsp;times as many &nbsp;10c coins as &nbsp;50c coins.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If he had &nbsp;$15.40 &nbsp;in total, &nbsp;how many &nbsp;50c coins did he have.

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Simple-arithmetic-word-problems-on-rate-of-work.lesson>Simple arithmetic word problems on "rate of work" </A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;A farmer ploughs his land in &nbsp;12 &nbsp;days if he uses &nbsp;5 &nbsp;tractors.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;25 &nbsp;men start a job which they can finish in &nbsp;40 &nbsp;days. &nbsp;After &nbsp;16 &nbsp;days &nbsp;10 &nbsp;men leave.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How many days in total did it take for the entire job to be finished?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;A certain job can be done by &nbsp;72 &nbsp;men in &nbsp;100 &nbsp;days. &nbsp;There were &nbsp;80 &nbsp;men at the start of the project

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;but after &nbsp;40 &nbsp;days, &nbsp;30 &nbsp;of them had to be transferred to another project.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How long will it take the remaining workforce to complete the job?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;Eight man take &nbsp;12 &nbsp;days to cultivate a piece of land.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;After working for &nbsp;3 &nbsp;days, &nbsp;10 &nbsp;more man were employed.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How long will it take to &nbsp;18 man &nbsp;to cultivate the rest of the land ?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 5. &nbsp;If &nbsp;18 &nbsp;pumps can raise &nbsp;2170 &nbsp;tons of water in &nbsp;10 &nbsp;days, &nbsp;working &nbsp;7 &nbsp;hours a day,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;in how many days will &nbsp;16 &nbsp;pumps raise &nbsp;1736 &nbsp;tons of water, &nbsp;working &nbsp;9 &nbsp;hours a day?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 6. &nbsp;Five workers have been hired to complete a job.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If one additional worker is hired, they could complete the job &nbsp;6 &nbsp;days earlier.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If the job needs to be completed &nbsp;32 &nbsp;days earlier, &nbsp;how many additional workers should be hired?

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Simple-and-simplest-arithmetic-Travel-and-Distanse-problems.lesson>Simple and simplest arithmetic Travel & Distance problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;A car moves from &nbsp;A &nbsp;to &nbsp;B &nbsp;at the rate of &nbsp;60 &nbsp;miles per hour.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It took &nbsp;4&nbsp; hours to reach &nbsp;B. &nbsp;Find the distance from &nbsp;A &nbsp;to &nbsp;B.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;The distance between the cities &nbsp;A &nbsp;and &nbsp;B is &nbsp;195 miles. A car moves from &nbsp;A &nbsp;to &nbsp;B

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;at the rate of &nbsp;65&nbsp; miles per hour. &nbsp;How long will it take for the car to reach &nbsp;B?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;The distance between the cities &nbsp;A&nbsp; and &nbsp;B&nbsp; is &nbsp;300 miles.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A car covered the distance from &nbsp;A&nbsp; to &nbsp;B&nbsp; in &nbsp;5 hours. &nbsp;Find the average speed of the car.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;A driver travels &nbsp;288 &nbsp;miles in &nbsp;6 &nbsp;hours. &nbsp;What is the average speed, &nbsp;in miles per hour?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 5. &nbsp;Two cars entered an Interstate highway at the same time and traveled toward each other

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The initial distance between the cars was &nbsp;390 miles. &nbsp;The first car was running

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;at the speed &nbsp;70 miles per hour, &nbsp;the second car was running at &nbsp;60 miles per hour.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 6. &nbsp;Two motorcycles travel toward each other from cities that are about &nbsp;950 km apart at rates of &nbsp;100 km/h&nbsp; and &nbsp;90 km/h.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;They started at  the same time. &nbsp;In how many hours will they meet?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 7. &nbsp;Two planes start from the same point and fly in opposite directions. &nbsp;One travels at &nbsp;475 mi/h &nbsp;and the other at &nbsp;525 mi/h.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 8. &nbsp;Ming left the hospital at the same time as &nbsp;Adam. &nbsp;They drove in opposite directions.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Adam drove at a speed of &nbsp;50 km. &nbsp;After two hours they were &nbsp;180 km apart. &nbsp;How fast did &nbsp;Ming drive ?

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Typical-arithmetic-Travel-and-Distance-problems.lesson>Typical arithmetic Travel & Distance problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;Two cars entered an Interstate highway at the same time at different locations and traveled&nbsp;&nbsp;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;in the same direction. &nbsp;The initial distance between cars was &nbsp;40&nbsp; miles.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;First car was running &nbsp;70&nbsp; miles per hour, &nbsp;the second car was running &nbsp;60&nbsp; miles per hour.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How long will it take for the first car to catch up the second one?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;A car leaves a city &nbsp;20 minutes after a truck leaves the same city.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The truck is traveling at an average speed of &nbsp;60 km/h and the car is traveling

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;at an average speed of &nbsp;80 km/h. &nbsp;How long will it take for the car to overtake the truck?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;A long-distance runner started on a course at an average speed of &nbsp;8 mph.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Half an hour later, &nbsp;a second runner began the same course at an average speed of &nbsp;10 mph.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How long after the second runner starts will the second runner overtake the first runner?

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Entertaining-catching-up-arithmetic-Travel-and-Distance-problems.lesson>Entertaining catching up arithmetic Travel & Distance problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;A wolf notices a hare 50 meters away and starts chasing the hare.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;At the same moment, the hare sees the wolf and starts running away.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The wolf runs at a speed of 4 meters per second. The hare runs at a speed of 3 meters per second.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;A patrol boat spots a poacher's boat and heads towards it; the poacher's boat tries to escape.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Both boats are moving in a straight line; the initial distance between them is 2 kilometers

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The poacher's boat is moving at 20 kilometers per hour. The patrol boat is moving at 24 kilometers per hour.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How long will it take the patrol boat to catch up with the poacher's boat?

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Other-basic-arithmetic-Travel-and-Distance-problems.lesson>Other basic arithmetic Travel & Distance problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;A train moves at the speed of &nbsp;36 kilometers per hour.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It takes for the train &nbsp;12 seconds to pass a telegraph post. &nbsp;Find the length of the train.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;A train has the length of &nbsp;96 meters. &nbsp;It moves uniformly with a constant speed.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It takes for the train &nbsp;12 seconds to pass a telegraph post. &nbsp;Find the speed of the train.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;A train which has a length of &nbsp;90 meters is traveling at a speed of &nbsp;36 kilometers per hour.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It passes a platform &nbsp;120&nbsp; meters long. &nbsp;How long does it take the train

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;to pass the platform from the moment the front of the train comes up to the closest end

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;of the platform to the moment the rear of the train comes up to the other end of the platform?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;A train which has a length of &nbsp;120 meters is traveling at a speed of &nbsp;54 kilometers per hour.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It passes a tunnel &nbsp;180&nbsp; meters long. &nbsp;How long does it take the train

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;to pass the tunnel from the moment the front of the train comes up to the closest end

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;of the tunnel to the moment the rear of the train comes up to the other end of the tunnel?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 5. &nbsp;It took a train &nbsp;65 seconds from starting to cross a bridge of length &nbsp;1440 m to completely pass over the bridge.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It also took the train &nbsp;75 seconds from when it entered a &nbsp;1680 m tunnel to completely pass through the tunnel.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 6. &nbsp;Two trains are approaching each other on parallel tracks. &nbsp;Train &nbsp;A &nbsp;is &nbsp;1/5 &nbsp;of a mile in length.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It travels east at a speed of &nbsp;40 &nbsp;mph.  Train &nbsp;B &nbsp;is &nbsp;1/8 &nbsp;of a mile in length. &nbsp;It travels west at a speed of &nbsp;50 mph.

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-word-problems-on-Travel-and-Distance.lesson>Advanced arithmetic word problems on Travel & Distance</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;You live &nbsp;20 &nbsp;miles from work and have &nbsp;25 &nbsp;minutes to get there and 3&nbsp;/4 &nbsp;of the trip

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is on the freeway. &nbsp;The other &nbsp;1/4 &nbsp;of the trip is in residential with the maximum speed of &nbsp;30 &nbsp;mph.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How fast would you need to drive on the freeway in order to make it on time?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;John and &nbsp;Lester were cycling towards the finish line. &nbsp;15 &nbsp;km from the end &nbsp;John passed Lester.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;John reached the end &nbsp;45 &nbsp;minutes earlier than Lester, &nbsp;who was still &nbsp;9 &nbsp;km from the end.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;Mary and &nbsp;Murray travel with some velocities heading directly towards each other across a distance of &nbsp;240 km.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If &nbsp;Murray starts at &nbsp;8 a.m. and &nbsp;Mary starts at &nbsp;10 a.m., &nbsp;they will meet at &nbsp;12:30 p.m.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Find their velocities.

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Finding-travel-time-and-average-rate.lesson>Finding travel time and average rate</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;Every day, &nbsp;Betty travels &nbsp;25 km from her apartment to the office.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;She travels &nbsp;20 kilometers by car at &nbsp;40 km/h, &nbsp;parks at the car park, &nbsp;and then walks at &nbsp;5 km/h

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;the rest of the way to work. &nbsp;If Betty leaves her home at &nbsp;6:30 a.m., &nbsp;at what time does she arrive at work?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;A delivery van traveled &nbsp;20 miles at an average speed of &nbsp;50 miles per hour.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Then it traveled &nbsp;10 miles at the average speed of &nbsp;20 miles per hour.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;A boat travels &nbsp;15 km/h in still water. &nbsp;This boat goes &nbsp;10 kilometers upstream in a river,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;which has the current rate of &nbsp;5 km/h, and then returns back downstream to its starting point.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(a) &nbsp;&nbsp;What is the travel time for the whole trip in?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(b) &nbsp;&nbsp;what is the average rate of the whole trip?

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Flying-back-and-forth.lesson>Flying back and forth</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;Joe and &nbsp;Frank want to meet each other half way between their cities. The distance between their towns is &nbsp;36 &nbsp;miles.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Both travel at &nbsp;6 &nbsp;miles per hour. &nbsp;Joe takes a carrier pigeon and sets it off toward &nbsp;Frank.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The pigeon travels at &nbsp;18 &nbsp;miles an hour. &nbsp;When it reaches &nbsp;Frank it turns around immediately and returns to &nbsp;Joe.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;What is the distance the pigeon covers when the two friends meet? &nbsp;The pigeon does not take a rest.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;Two bees leave simultaneously two locations &nbsp;150 &nbsp;meters apart and fly, &nbsp;without stopping,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;back and forth between these two locations at average speeds of &nbsp;3 &nbsp;meters per second and &nbsp;5 &nbsp;meters per second, &nbsp;respectively.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(a) &nbsp;&nbsp;How long is it until the bees meet for the first time?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(b) &nbsp;&nbsp;How long is it until they meet for the second time?

To see the whole list of lessons on arithmetic problems, &nbsp;use this link &nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Arithmetic-problems-YOUR-ONLINE-TEXTBOOK.lesson>Arithmetic problems - YOUR ONLINE TEXTBOOK</A>

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