Suppose that a cyclist began a 544 mi ride across a state at the western edge of the​ state, at the same time that a car traveling toward it leaves the eastern

Question

Suppose that a cyclist began a 544 mi ride across a state at the western edge of the state, at the same time that a car traveling toward it leaves the eastern end of the state. If the bicycle and car met after 8.5 hr and the car traveled 31.2 mph faster than the bicycle, find the average rate of each.

Answer 1

Let B = bike speed and C = car speed

 

Translate the English into math:

C = B + 31.2

(B + C)8.5 = 544

Substitute

(B + B + 31.2)8.5 = 544

Divide by 8.5

2B + 31.2 = 64

Subtract 31.2 from each side

2B = 32.8  => B = 16.4  and C = 47.6

 

You should take these answers and make sure they corectly solve the problem as stated.