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?

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Let r = speed of slower car

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

Start with the distance-rate-time equation.


Plug in (since the slower car goes 352 miles)


Divide both sides by "r" to isolate "t".


Rearrange the equation


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


Start with the distance-rate-time equation.


Plug in (since the faster car went 456 miles)


Replace "r" with "r+13" (since the faster car goes 13 mph faster


Plug in (the previous equation we isolated)


Rearrange the terms.


Multiply both sides by "r".


Distribute.


Subtract from both sides.


Combine like terms on the left side.


Divide both sides by to isolate .


Reduce.


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Answer:

So the solution is


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