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# Recent problems solved by 'josmiceli'

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 Travel_Word_Problems/644082: At noon a train leaves Washington, D.C., headed for Charleston, South Carolina, a distance of 500 mi. The train travels at a speed of 60 mph. At 1 P.M. a second train leaves Charleston headed for Washington, D.C., traveling at 50 mph. How long after the train leaves Charleston will the two trains pass each other? 1 solutions Answer 404802 by josmiceli(9671)   on 2012-08-31 18:07:02 (Show Source): You can put this solution on YOUR website!The 60 mi/hr train has a 1 hr head start The head start is mi Let = distance that 60 mi/hr train travels after stopwatch starts until they meet Let = time in hrs on stopwatch after 50 mi/hr train leaves --------- Start a stop watch when the 50 mi/hr train leaves. They both will now travel for the same amount of time. --------- 60 mi/hr train's equation: (1) 50 mi/hr train's equation: (2) ----------------------- Substitute (1) into (2) (2) (2) (2) (2) 4 hours after the 50 mi/hr train leaves Charleston they will meet check: (1) (1) and (2) (2) (2) (2) Note that 240 + 200 + 60 = 500 as it should
 Linear-equations/644067: The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May her driving cost was \$350 for 420 mi and in June her cost was \$470 for 900 mi. Assume that there is a linear relationship between the monthly cost C of driving a car and the distance driven d. (a) Find a linear equation that relates C and d.1 solutions Answer 404785 by josmiceli(9671)   on 2012-08-31 16:34:57 (Show Source): You can put this solution on YOUR website!The general form of the equation is where is the slope Plot on the vertical axis Plot on the horizontal Slope is ( change in C ) / ( change in d ) ------------------ Now just plug in one of the 2 given points to find , the intercept on the vertical axis ------------ The equation is check answer: Here's the plot:
 Travel_Word_Problems/643970: John is three times as far from the finish line as he is from starting point of a 10-km race How far has he run?1 solutions Answer 404737 by josmiceli(9671)   on 2012-08-31 09:46:28 (Show Source): You can put this solution on YOUR website!Let = distance from starting point given: km He has run 2.5 km
 test/643959: A large container of water is 7/8 full. After 15 l has been taken out the container is 2/3 full. When full, how many litres does the container hold1 solutions Answer 404736 by josmiceli(9671)   on 2012-08-31 09:41:37 (Show Source): You can put this solution on YOUR website!Let = liters when full given: Multiply both sides by It holds 72 liters when full
 Mixture_Word_Problems/643971: how many quarts of pure antifreeze must be added to 2 quarts of a 10% antifreeze solution to obtain a 50% solution?1 solutions Answer 404735 by josmiceli(9671)   on 2012-08-31 09:32:39 (Show Source): You can put this solution on YOUR website!Let = quarts of pure antifreeze needed quarts of pure antifreeze in 10% solution 1.6 quarts of pure antifreeze must be added check: OK
 Trigonometry-basics/643725: the line through (8,-2) and perpendicular to the line y=-2x+71 solutions Answer 404607 by josmiceli(9671)   on 2012-08-30 18:50:14 (Show Source): You can put this solution on YOUR website!The slope of the line is When the slope is , the slope that is perpendicular is The point-slope form is The point (8,-2) is included --------- The equation is
 Linear-equations/643701: How do you write in standard form an equation of the line with the given slope through the given point? Ex. slope = -4; (2,2)1 solutions Answer 404606 by josmiceli(9671)   on 2012-08-30 18:29:42 (Show Source): You can put this solution on YOUR website!Start off with the point-slope form of the equation which is: (x,y) = (2,2) ---------- The equation in point-slope form is In standard form it is -------------- check: OK
 Sequences-and-series/643622: find the sum of the whole number from 1 to 99991 solutions Answer 404554 by josmiceli(9671)   on 2012-08-30 16:11:09 (Show Source): You can put this solution on YOUR website!First do a shorter sequence to get the right method. First find the sum of 0 to 10 ( I did it on my calculator ) This is How about This is ---------------------- So, the formula is: The sum of the numbers from 1 to n = ---------------
 Functions/643625: Given the function f(x)=2x+3, find each of the following f(10),f(-10),f(0) f(10)= f(-10)= f(0)=1 solutions Answer 404550 by josmiceli(9671)   on 2012-08-30 15:54:41 (Show Source): You can put this solution on YOUR website!f(x)=2x+3, --------- ------------ --------------
 Rate-of-work-word-problems/643510: 2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?1 solutions Answer 404504 by josmiceli(9671)   on 2012-08-30 10:32:42 (Show Source): You can put this solution on YOUR website!Add their rates of painting ( 1 house / 4 hrs ) + ( 1 house / 6 hrs ) = 1 house / x hrs Multiply both sides by hrs = minutes Working together, they can paint the house in 2 hrs 24 min
 Complex_Numbers/643502: Need help trying to find real solutions of this equation x^9 = 125x^61 solutions Answer 404502 by josmiceli(9671)   on 2012-08-30 10:00:36 (Show Source): You can put this solution on YOUR website! Divide both sides by
 Age_Word_Problems/643220: My daughter is twice is old as my son and 1/2 as old as I am. In 22 years my son will be half my age. how old is my daughter?1 solutions Answer 404417 by josmiceli(9671)   on 2012-08-29 20:27:46 (Show Source): You can put this solution on YOUR website!Let = my age Let = my Daughter's age Let = my Son's age given: (1) (2) (3) -------------------------- (1) (2) Substitute (1) and (2) into (3) (3) multiply both sides by (3) (3) (3) My daughter is 22 check: (1) (1) and (2) (2) ------------ (3) (3) (3)
 Mixture_Word_Problems/643244: How do I put 45% of a mixture in algebraic form?1 solutions Answer 404411 by josmiceli(9671)   on 2012-08-29 20:07:24 (Show Source): You can put this solution on YOUR website!Call the total mixture 45% of the mixture is
 test/643059: how would i solve R in this equation 15.5=( R) to the 161 power1 solutions Answer 404317 by josmiceli(9671)   on 2012-08-29 16:51:00 (Show Source): You can put this solution on YOUR website! Take the log of both sides check: close enough
 Money_Word_Problems/642961: You get a weekly rate of \$485 for a car with no mileage charge. You spend \$102.65 on gasoline costs and drive 483 miles. True or False: The total cost per mile is \$0.99. true or false? any help be great :) thanks!1 solutions Answer 404291 by josmiceli(9671)   on 2012-08-29 13:35:03 (Show Source): You can put this solution on YOUR website!Your total cost is Cost per mile = the cost per mile is \$1.22 false
 Travel_Word_Problems/642928: A car rents for \$35 per day plus 18 cents per mile. You are on a daily budget of \$71. What mileage will allow you to stay within your budget?1 solutions Answer 404288 by josmiceli(9671)   on 2012-08-29 13:24:18 (Show Source): You can put this solution on YOUR website!Let = number of miles driven per day given: 200 miles driven will be within the budget
 Human-and-algebraic-language/642938: Three years from now, Judith will be y years old. How old was she 4 years ago?1 solutions Answer 404284 by josmiceli(9671)   on 2012-08-29 12:54:38 (Show Source): You can put this solution on YOUR website!Her age now is 4 years ago, her age was
 Travel_Word_Problems/642940: a bike rider is traveling at a speed of 15 feet per second. Write an expression for the distance traveled after s seconds. Make a table that records the distance for 3.0,5.8, and 14.0 seconds.1 solutions Answer 404283 by josmiceli(9671)   on 2012-08-29 12:52:32 (Show Source): You can put this solution on YOUR website! ----------- s: 3.0 sec d: 45 ft ------- s: 5.8 sec d: 87 ft ------- s: 14.0 sec d: 210 ft
 Square-cubic-other-roots/642937: THE AREA OF A SQUARE FIELD IS 422500SQ.METER HOW MUCH STRING IS REQUIRED FOR FIXING ALONG THE SIDES AS A FENCE1 solutions Answer 404282 by josmiceli(9671)   on 2012-08-29 12:44:48 (Show Source): You can put this solution on YOUR website!Equation for area is Equation for perimeter is where is the length of a side given: m2 m and m 2,600 meters of string is needed
 Equations/642617: find equation for horizontal contains points (8,2)1 solutions Answer 404157 by josmiceli(9671)   on 2012-08-28 20:20:25 (Show Source): You can put this solution on YOUR website!Every point on a horizontal line has the form (x,y[1]) where can be any value and is a constant (8,2) means that no matter what is so is the equation
 Mixture_Word_Problems/642363: British sterling silver is a copper-silver alloy that is 7.5% copper by weight. How many grams of pure copper and how many grams of British sterling silver should be used to prepare 240 grams of a copper-silver alloy that is 16% copper by weight?1 solutions Answer 404087 by josmiceli(9671)   on 2012-08-28 16:23:17 (Show Source): You can put this solution on YOUR website!Let grams of pure copper needed = Let grams of British sterling silver needed = = grams of copper in British sterling silver needed -------------------- (1) (2) ------------------- (2) (2) (2) Substitute this into (1) (1) (1) (1) 22.05 grams of pure copper are needed 217.95 grams of British sterling silver are needed check: (1) (1) (1) (1) OK
 Linear-equations/642377: i need to know what vertical and horizontal intercepts are1 solutions Answer 404079 by josmiceli(9671)   on 2012-08-28 15:59:31 (Show Source): You can put this solution on YOUR website!The x-intercept occurs where The y-intercept occurs where -------------------------------- There can be more than one x-intercept, but there can be only one y-intercept ------------------------------- Suppose you have the equation To find the x-intercept(s), ---------- And, to find the y-intercept, ---------- Here's the plot:
 Travel_Word_Problems/642315: If there is a 500 mile race the driver is 90 miles closer to the finish line than the start , how far has the driver traveled ?1 solutions Answer 404034 by josmiceli(9671)   on 2012-08-28 13:12:30 (Show Source): You can put this solution on YOUR website!Let = his distance from the start = his distance from the finish given: The driver has traveled 295 miles check: and OK
 Travel_Word_Problems/642166: Bob runs 3 miles in 25 minutes. At the same rate, how many miles would he run in 60 minutes?1 solutions Answer 403974 by josmiceli(9671)   on 2012-08-28 02:01:37 (Show Source): You can put this solution on YOUR website!( 3 miles / 25 min ) = ( 3/25) mile / 1 min He can run 7.2 miles in 60 minutes
 Rectangles/642069: it takes 7 yards of material to make 3 jackets. You brought 15 yards of material to make 7 jackets. Did you buy the right amount of material? if not, how much over or under where you? explain1 solutions Answer 403950 by josmiceli(9671)   on 2012-08-27 21:05:54 (Show Source): You can put this solution on YOUR website!( 7 yds ) / ( 3 jackets ) = (7/3) yds / ( 1 jacket ) To make 7 jackets, You need 16 and 1/3 yards of material to make 7 jackets, so 15 yds is not enough
 Age_Word_Problems/642051: In January of the year 2000, my wife lisa was eleven times as old as my son Don. In January 2012, she will be three times as old as my son. How old was my son in January of 2000?1 solutions Answer 403945 by josmiceli(9671)   on 2012-08-27 20:57:53 (Show Source): You can put this solution on YOUR website!Let = Son's age in Jan 2000 Let = Lisa's age in 2000 = Lisa's age in Jan 2000 When Son is , Lisa is ------------------------ (1) (2) ------------------------ Substitute (1) into (2) (2) (2) (2) (2) (2) and (1) (1) Your Son was 3 in Jan 2000 check: (2) (2) (2) (2) OK
 Geometry_Word_Problems/642025: The measure of the supplement of an angle is 60 less than three times the measure of the complement of the angle. Find the measure of the angle.1 solutions Answer 403932 by josmiceli(9671)   on 2012-08-27 20:10:47 (Show Source): You can put this solution on YOUR website!Call the angle The supplement = The complement = given: The angle is 15 degrees
 Word_Problems_With_Coins/642011: A man has 19 coins in his pocket, all of which are dimes and quarters. If the total value of his change is \$ 3.25, how many dimes and how many quarters does he have?1 solutions Answer 403930 by josmiceli(9671)   on 2012-08-27 20:04:21 (Show Source): You can put this solution on YOUR website!he has dimes and quarters given: ( in cents ) He has 10 dimes and 9 quarters check: OK
 percentage/641756: 99 is 45% of what # 1 solutions Answer 403782 by josmiceli(9671)   on 2012-08-27 11:15:11 (Show Source): You can put this solution on YOUR website! 99 is 45% of 220
 �t�e�s�t/641755: Two certificates of deposit pay interest rates that differ by 2%. For the first CD, the money is invested for a year and earns \$200 interest. For the second CD the same amount of money invested earns \$255 in a year. What is the interest rate of the first CD account (rounded to the nearest tenth)?1 solutions Answer 403781 by josmiceli(9671)   on 2012-08-27 11:13:23 (Show Source): You can put this solution on YOUR website!Let = the speed of the current = dog's speed going downstream = dog's speed going upstream Let = dog's time to travel downstream = dog's time to travel upstream --------------------------------- Equation going downstream: (1) Equation going upstream: (2) ------------------------ (1) and (2) Substitute (1) into (2) (2) (2) Multiply both sides by (2) Multiply both sides by (2) (2) (2) (2) The speed of the current is 2 mi/hr check: (1) (1) (1) hrs and (2) (2) (2) hrs OK- I get the same answer