SOLUTION: One car travels 20mph faster than another. While one of them travels 240 miles, the other travels 180 miles. Find the speed of both. I do know that we are looking for the ra

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Question 224089: One car travels 20mph faster than another. While one of them travels 240 miles, the other travels 180 miles. Find the speed of both.

I do know that we are looking for the rate which is distance divided by time, but I am having problems setting it up.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Time of one car is equal to time of the other car, where time is t=D%2Fr.

Let x = speed of slower car (which travels the shorter distance!)
x+20 = speed of faster car (which travels the longer distance!)

D%2Fr=D%2Fr
240%2F%28x%2B20%29=180%2Fx

Remember that a%2Fb=c%2Fd means ad=bc.

Likewise 240%2F%28x%2B20%29=180%2Fx means 240x=180%28x%2B20%29
240x=180x%2B3600

Subtract 180x from each side:
60x=3600
x=60 mph speed of slower car
x%2B20=80 mph speed of faster car

Check: The faster car travels 240 miles at 80 mph = 3 hours
The slower car travels 180 miles at 60 mph = 3 hours.

R^2

Dr. Robert J. Rapalje