SOLUTION: One car travels 13miles per hour faster than another. in the time it takes the slower car to travel 352 miles, the faster travels 456 mile. Find the sped of both cars?

Algebra ->  Systems-of-equations -> SOLUTION: One car travels 13miles per hour faster than another. in the time it takes the slower car to travel 352 miles, the faster travels 456 mile. Find the sped of both cars?      Log On


   

Question 202359: One car travels 13miles per hour faster than another. in the time it takes the slower car to travel 352 miles, the faster travels 456 mile. Find the sped of both cars?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let r = speed of slower car

First, let's set up the equation for the slower car

d=rt Start with the distance-rate-time equation.


352=rt Plug in d=352 (since the slower car goes 352 miles)


352%2Fr=t Divide both sides by "r" to isolate "t".


t=352%2Fr Rearrange the equation


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Now let's set up the equation for the faster car


d=rt Start with the distance-rate-time equation.


456=rt Plug in d=456 (since the faster car went 456 miles)


456=%28r%2B13%29%2At Replace "r" with "r+13" (since the faster car goes 13 mph faster


456=%28r%2B13%29%2A%28352%2Fr%29 Plug in t=352%2Fr (the previous equation we isolated)


456=%28352%2Fr%29%28r%2B13%29 Rearrange the terms.


456r=352%28r%2B13%29 Multiply both sides by "r".


456r=352r%2B4576 Distribute.


456r-352r=4576 Subtract 352r from both sides.


104r=4576 Combine like terms on the left side.


r=%284576%29%2F%28104%29 Divide both sides by 104 to isolate r.


r=44 Reduce.


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Answer:

So the solution is r=44


This means that the slower car is going 44 mph and the faster car is going 44+13=57 mph