Tutors Answer Your Questions about Travel Word Problems (FREE)
Question 1163988: A family is on a road trip. The speed limit during the first 115 miles of the trip is 65 mph, and the speed limit during the last 165 miles is 75 mph. How many miles per hour over the speed limits must they drive in order to arrive at their destination in 3.5 hours?
Click here to see answer by MathTherapy(10549)   |
Question 1164038: Danny is taking a road trip. After 36 miles, he reaches a stretch of highway with a speed limit of 60 miles/hour. Danny is trying to figure out the minimum number of hours he’ll need to drive to reach over 300 total miles for the trip, assuming he stays under or at the speed limit.
He creates the inequality 60t + 36 ≥ 300, where t is the time elapsed, in hours.
What statement is the most accurate?
Click here to see answer by ikleyn(52754)  |
Question 1164038: Danny is taking a road trip. After 36 miles, he reaches a stretch of highway with a speed limit of 60 miles/hour. Danny is trying to figure out the minimum number of hours he’ll need to drive to reach over 300 total miles for the trip, assuming he stays under or at the speed limit.
He creates the inequality 60t + 36 ≥ 300, where t is the time elapsed, in hours.
What statement is the most accurate?
Click here to see answer by josgarithmetic(39613) |
Question 1164241: Two trucks leave a warehouse at the same time. One travels due east at an average speed of 62 miles per hour, and the other travels due west at an average speed of 47 miles per hour. After how many hours will the two trucks be 763 miles apart?
Click here to see answer by greenestamps(13195)  |
Question 1164293: amanda drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Amanda drove home, there was no traffic and the trip only took 5 hours. If her average rate was 18 miles per hour faster on the trip home, how far away does Amanda live from the mountains?
Click here to see answer by greenestamps(13195) |
Question 1164293: amanda drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Amanda drove home, there was no traffic and the trip only took 5 hours. If her average rate was 18 miles per hour faster on the trip home, how far away does Amanda live from the mountains?
Click here to see answer by Theo(13342)  |
Question 1164293: amanda drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Amanda drove home, there was no traffic and the trip only took 5 hours. If her average rate was 18 miles per hour faster on the trip home, how far away does Amanda live from the mountains?
Click here to see answer by josgarithmetic(39613) |
Question 1164262: Derrick and his family plan to drive 570 miles from their home outside
Memphis to Chicago over the summer break. They agree to leave at 8:00 am.
However, his dad can’t find the car keys, and they start 2 hours late.
a. Using information from the graph below, create an equation that represents the relationship between time and distance for the summer break trip and explains the meaning of the terms in the equation. The x-axis is miles in intervals of 60, and the y-axis is time with intervals of 1 hour. The points on the graph are (0,2) (60,3) (120,4) (180,5) (240,6) (300,7)
Click here to see answer by solver91311(24713)  |
Question 1164303: Jerry’s parents live 55.0 km exactly west from his home. On one trip from his house to his parent’s home, he takes 1.25 hrs. to complete the journey. On arrival, he forgot he had to pick up some groceries, and so immediately, he drives 22.0 km east to a grocery store in a time of 0.40 hrs. Determine the average speed of Jerry (in units of m/s) for his entire trip from his home to the grocery
store.
Click here to see answer by Shin123(626)  |
Question 1164303: Jerry’s parents live 55.0 km exactly west from his home. On one trip from his house to his parent’s home, he takes 1.25 hrs. to complete the journey. On arrival, he forgot he had to pick up some groceries, and so immediately, he drives 22.0 km east to a grocery store in a time of 0.40 hrs. Determine the average speed of Jerry (in units of m/s) for his entire trip from his home to the grocery
store.
Click here to see answer by ikleyn(52754) |
Question 1164424: Jim began a 206-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 6 hours. If Jim walks at a rate of 5 miles per hour and rides at 37 miles per hour, find the amount of time he spent on the bicycle.
Click here to see answer by Theo(13342) |
Question 1164424: Jim began a 206-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 6 hours. If Jim walks at a rate of 5 miles per hour and rides at 37 miles per hour, find the amount of time he spent on the bicycle.
Click here to see answer by MathTherapy(10549) |
Question 1164426: Lewiston and Vernonville are 144 miles apart. A car leaves traveling towards Vernonville, and another car leaves Vernonville at the same time, traveling towards Lewiston . The car leaving averages 10 miles per hour more than the other, and they meet after 1 hour and 36 minutes. What are the average speeds of the cars?
Click here to see answer by ikleyn(52754) |
Question 1164425: Two towns are 1050 miles apart. A group of hikers start from each town and
walk the trail toward each other. They meet after a total hiking time of 200
hours. If one group travels 1 1/2 mile per hour faster than the other group,
find the rate of each group.
Click here to see answer by ikleyn(52754) |
Question 1164425: Two towns are 1050 miles apart. A group of hikers start from each town and
walk the trail toward each other. They meet after a total hiking time of 200
hours. If one group travels 1 1/2 mile per hour faster than the other group,
find the rate of each group.
Click here to see answer by Edwin McCravy(20054)  |
Question 1164423: Thaddeus and Ian start at the same location and drive in opposite directions, but leave at different times. When they are 635 miles apart, their combined travel time is 12 hours. If Thaddeus drives at a rate of 50 miles per hour and Ian drives at a rate of 55 miles per hour, how long had each been driving?
Click here to see answer by Boreal(15235)  |
Question 1164438:
Mr. Williams asks his Algebra I class to find the solutions to an equation in two variables with the set of real numbers.
Colton correctly creates the table below using values from the domain of the equation. He then uses this table to create a graph.
The coordinates on the table and graphs are (0,-4)(2,-1.5)(-2,-6.5)(5,2.25)(-8,-14)(10,8.5)
Determine the equation Colton used to create the table. Use mathematical reasoning to justify that the equation is correct. The equation Colton used is f(x)= 1.25x -4. The equation is correct because to get that exact table and graph this equation is the only one that can achieve that according to the work below.
m=y2-y1 / x2-x1
m= 8.5-2.25 / 10-5
m= 6.25 / 5
m= 1.25.
Destiny sees Colton’s work and argues that any table contains some but not all of the solutions to Mr. Williams’ equation. Do you agree or disagree with Destiny? Explain why or why not.
Click here to see answer by josgarithmetic(39613) |
Question 1164436: A room with dimensions 20 feet by 26 feet is to be used to host a meeting. Under the CDC guidelines, we need to design the seats to be six feet apart. John suggested to put people in rows, with the first row facing the others, and to be used by the hosts.
How many rows can be used and what is the maximum number of people that can fit? (Hint: Make sure that the distance between any 2 consecutive points is exactly 6 feet.)
Janet suggested to put the attendees on a parabola-like setting, with the zeros of the function on one edge of the room. The vertices of the parabolas should also be 6 feet apart.
How many parabolas can you fit? Write the functions for each one.
Assume that the first point on the curve is 0, 0. Use the distance formula and your functions from part (b) to find the next possible point with a safe distance of six feet.
Write a rule to find the next consecutive points on the parabola with a safe distance.
How many people can you fit in the room if they are only allowed to sit on the designated parabolas?
Can we add more attendees to the room while keeping a safe distance? Create a graphical design for the room to maximize the number of attendees.
Is it possible to fit more attendees if they are required to sit on a circular arrangement? Create circles that are six feet apart to maximize the number of attendees. Find the coordinates of three consecutive seats on each arrangement.
Click here to see answer by ikleyn(52754) |
Question 1164439: Farmer Bob would like to plant six additional fields of produce in another part of his property. Find the dimensions of each field, in terms of x, given their area.
Strawberry field with area 16x2+4x
A= L x W
16x^2+4x=L x W
16x^2+4x= 4x(4x+1)
L= 4x+1
W=4x
Cucumber field with area x2-4x-21
A= L x W
x^2-4x-21=L x W 21=7x3
x^2-7x+3x-21= L x W
(x^2-7x)+(3x-21)= L x W
x(x-7)+3(x-7)=L x W
(x-7)(x-3) = L x W
L= x-7
B=x-3
Tomato field with area x2-36
A=L x W
a^2-b^2=(a+b)(a-b)
x^2-36=L x W
x 6
(x+6)(x-6)= L x W
L=x+6
W=x-6
Parsley field with area x2-10x+21
A=L x W
x^2-10x+21=L x W 21=3x7
x^2-3x-7x+21=L x W
(x^2-3x)-(7x+21)=L x W
x(x-3)-7(x-3)=L x B
(x-3)(x-7)=L x B
L=x-3
W=x-7
Onion field with area x2-11x+30
A=L x W
x^2-11x+30=L x W 30=6x5
x^2-6x-5x+30=L x W
(x^2-6x)-(5x+30)=L x W
x(x-6)-5(x-6)=L x W
(x-5)(x-6)=L x W
L=x-5
W=x-6
Watermelon field with area x2+8x-20
A=L x W
x^2+8x-20=L x W 20=10x2
x^2+10x-2x-20=L x W
(x^2+10x)-(2x-20)=L x W
x(x+10)-2(x+10)=L x W
(x+10)(x-2)=L x W
L=x+10
W=x-2
What values of x cannot be used if the above six fields are to be built together?
Click here to see answer by ikleyn(52754) |
Question 1164435: On March 1st, 2012 of her freshman year at Science Park High School, Jessica started working 2 jobs after school. (She is working in her parents’ store and does not need working papers.) She works the same number of hours every week. Jessica decided to save all her money to purchase a new car after she graduates.
After five weeks of work, she had $1,570 saved. After ten weeks, she saved $2,453.
Write a function that represents Jessica’s savings.
x= weeks y=money earned
Coordinates: (5,1570)(10,2453) y=mx+b
m=y2-y1 / x2-x1 y=176.6x+b
m=2453-1570 / 10-5 2453=176.6(10)+b
m=88/5 2453=1766+b
m=176.6 - 1766 -1766
687=b
f(x)=176.6x+687.
At the beginning of the 53rd week, Jessica decided to stop working and invest all her savings in a corporate bond. The bond pays 9% interest compounded quarterly. Jessica decided to invest the money for a period of 2 years. Note that Jessica cannot withdraw money or sell the corporate bond before the end of the term.
Write a function that models her investment.
P= f(x)=176.6x+687.
P= 176.6(53)+687
P= 10,046.8
y=a(b)^x
y=10,046.8(1+0.09)^2
y=10,046.8(1.09)^2
y=10,046.8(1.1881)
y=11,936.60308 ~11,936.60
At the end of the 2-year investment, Jessica decided to purchase a new car for $18,000. It will be financed over a period of 48 months with 0% interest.
If she put $2,000 as down payment, how much does she need to pay each month?
Turns out that this was a lucky car for Jessica! The day she signed the purchase agreement and drove it out of the lot, she got her long-awaited surprise. Jessica got accepted to MIT! She was required to move in after 5 months from receiving the acceptance letter. As she moved to Cambridge, she decided to take a job that pays $3,200 a month. Her employer will deduct 12.6% in taxes from her paycheck. She also has a grant that pays all her university tuition. However, she needs to rent a studio for $1,500 per month, including utility. She estimated that her living expenses will cost $347 per week.
With her monthly car payments in mind, create a function of her savings during her 4 years at Cambridge, MA. How much money would she have at the end of her 4 years residency in Massachusetts?
Graph Jessica’s savings since she started working until her graduation from MIT in May 2020.
Click here to see answer by ikleyn(52754) |
Question 1164434: Shannon was so happy coming back with her brand new PS5 pre-order. She was able to order from the only store that lists a price: Play N Trade Vancouver. The listed price is CA$560 (Canadian dollars). Each Canadian dollar is worth 73 US cents.
Luckily, Shannon was able to find a 20% off coupon for one item purchased
from Play N Trade Vancouver. In addition, she received a 15% off offer for
applying for a new credit card.
Shannon had to pay the 7% provincial sales tax on the initial price before discounts and 5% Goods and Services tax on the discounted price. She must also pay 12% for shipping and handling fees on the final bill including taxes.
How much did Shannon pay (in USD) in total?
CA$1=$0.73
Price = CA$560 =$408.80
Shannon paid: $408.80 -0.20(408.80) - 0.15(408.80)
408.80-81.76-61.32
$265.72+0.07(408.80)+0.05(265.72)
265.72+28.616+13.286
265.72+28.62+13.29
307.63+0.12(307.63)
307.63+36.9156
344.5456~ 344.54.
Shannon paid US$344.54 in total.
Jose, Shannon’s significant other, decided to get a PS5 for himself. He paid a total of $375.46.
Although Jose received some discounts, he did not get the same discounts as Shannon. What percentage discount did Jose get?
To promote the sale of PS5, Sony stated a campaign in the US promising 17% discount and 12% loyal customers additional discount. Since NJ charges only 6.625% sales tax, Sony promised its NJ customers to pay only $346.25 for the unit. However, Sony did not list the original price in this promotion.
Calculate the missing list price that Sony will offer to its NJ residents. How much does Sony lose per unit of potential income due to the discount?
Click here to see answer by ikleyn(52754) |
Question 1164552: Danny is taking a road trip. After 36 miles, he reaches a stretch of highway with a speed limit of 60 miles/hour. Danny is trying to figure out the minimum number of hours he’ll need to drive to reach over 300 total miles for the trip, assuming he stays under or at the speed limit.
He creates the inequality 60t + 36 ≥ 300, where t is the time elapsed, in hours.
What statement is the most accurate?
A.
Danny needs at least 7 hours to drive 300 miles.
B.
Danny may drive 300 miles in 5 hours.
C.
At 4 hours, Danny will have just driven 300 miles.
D.
It isn’t possible to drive 300 miles before the day is over.
Click here to see answer by Theo(13342) |
Question 1164674: Jonah’s family went on a vacation. They drove for 2.75 hours, stopped for half an hour to have lunch, then drove for another 2.6 hours. They arrived at their destination at 5:00 pm. At what time did the family leave their home? (Give the exact time.)
Click here to see answer by josgarithmetic(39613) |
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20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 27136..27180, 27181..27225, 27226..27270, 27271..27315, 27316..27360, 27361..27405, 27406..27450, 27451..27495, 27496..27540, 27541..27585, 27586..27630, 27631..27675, 27676..27720, 27721..27765, 27766..27810, 27811..27855, 27856..27900, 27901..27945, 27946..27990, 27991..28035, 28036..28080, 28081..28125, 28126..28170, 28171..28215, 28216..28260, 28261..28305, 28306..28350, 28351..28395, 28396..28440, 28441..28485, 28486..28530, 28531..28575, 28576..28620, 28621..28665, 28666..28710, 28711..28755, 28756..28800, 28801..28845, 28846..28890, 28891..28935, 28936..28980, 28981..29025, 29026..29070, 29071..29115, 29116..29160, 29161..29205, 29206..29250, 29251..29295, 29296..29340, 29341..29385, 29386..29430, 29431..29475, 29476..29520, 29521..29565, 29566..29610, 29611..29655, 29656..29700, 29701..29745, 29746..29790, 29791..29835, 29836..29880, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240, 30241..30285, 30286..30330, 30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690, 30691..30735, 30736..30780, 30781..30825, 30826..30870, 30871..30915, 30916..30960, 30961..31005, 31006..31050, 31051..31095, 31096..31140, 31141..31185, 31186..31230, 31231..31275, 31276..31320, 31321..31365, 31366..31410, 31411..31455, 31456..31500, 31501..31545, 31546..31590, 31591..31635, 31636..31680, 31681..31725, 31726..31770, 31771..31815, 31816..31860, 31861..31905, 31906..31950, 31951..31995, 31996..32040, 32041..32085, 32086..32130, 32131..32175, 32176..32220, 32221..32265, 32266..32310, 32311..32355, 32356..32400, 32401..32445, 32446..32490, 32491..32535, 32536..32580, 32581..32625, 32626..32670, 32671..32715, 32716..32760, 32761..32805, 32806..32850, 32851..32895, 32896..32940, 32941..32985, 32986..33030, 33031..33075, 33076..33120, 33121..33165, 33166..33210, 33211..33255, 33256..33300, 33301..33345, 33346..33390, 33391..33435, 33436..33480, 33481..33525, 33526..33570, 33571..33615, 33616..33660, 33661..33705, 33706..33750, 33751..33795, 33796..33840, 33841..33885, 33886..33930, 33931..33975, 33976..34020, 34021..34065, 34066..34110, 34111..34155, 34156..34200, 34201..34245, 34246..34290, 34291..34335, 34336..34380, 34381..34425, 34426..34470, 34471..34515, 34516..34560, 34561..34605, 34606..34650, 34651..34695, 34696..34740, 34741..34785, 34786..34830, 34831..34875, 34876..34920, 34921..34965, 34966..35010, 35011..35055, 35056..35100, 35101..35145, 35146..35190, 35191..35235, 35236..35280, 35281..35325, 35326..35370, 35371..35415, 35416..35460, 35461..35505, 35506..35550, 35551..35595, 35596..35640, 35641..35685, 35686..35730, 35731..35775, 35776..35820, 35821..35865, 35866..35910, 35911..35955, 35956..36000, 36001..36045, 36046..36090, 36091..36135, 36136..36180, 36181..36225, 36226..36270, 36271..36315, 36316..36360, 36361..36405, 36406..36450, 36451..36495, 36496..36540, 36541..36585, 36586..36630, 36631..36675, 36676..36720, 36721..36765, 36766..36810, 36811..36855, 36856..36900, 36901..36945, 36946..36990, 36991..37035, 37036..37080, 37081..37125, 37126..37170, 37171..37215, 37216..37260, 37261..37305, 37306..37350, 37351..37395, 37396..37440, 37441..37485, 37486..37530, 37531..37575, 37576..37620
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