SOLUTION: A van​ averages 9 miles per hour faster than a car. If the van travels 100 miles in the same time it takes the car​ to travel 70 miles, then what is the speed of each?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A van​ averages 9 miles per hour faster than a car. If the van travels 100 miles in the same time it takes the car​ to travel 70 miles, then what is the speed of each?      Log On


   

Question 1125034: A van​ averages 9 miles per hour faster than a car. If the van travels 100 miles in the same time it takes the car​ to travel 70 miles, then what is the speed of each?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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A van​ averages 9 miles per hour faster than a car. If the van travels 100 miles in the same time it takes the car​ to travel 70 miles, then what is the speed of each?
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A van​ averages k miles per hour faster than a car. If the van travels D miles in the same time it takes the car​ to travel d miles, then what is the speed of each?
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(Note very carefully, d%3C%3ED ). 

Unknowns:  x and r

           SPEED          TIME         DISTANCE
VAN         r+k           x=D/(r+k)        D
CAR         r             x=d/r            d

D%2F%28r%2Bk%29=d%2Fr
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d%28r%2Bk%29=Dr
dr%2Bdk=Dr
Dr-dr=dk
r%28D-d%29=dk
highlight%28r=%28dk%29%2F%28D-d%29%29-----substitute your given values.