Speed, time and distance

Question

Suppose a cyclist began a 646 mi ride across a state at the western edge of the state. At the same time that a car traveling towards it leaves the eastern end of the state. If the bicycle and car met at 9.5 hr and the car traveled 33.4 mph faster than the bicycle, find the average rate of each

Answer 1

Let r = cyclist's rate and then r+33.4 = rate of the car

9.5r + 9.5(r+33.4) = 646, i.e. the distance traveled by the cyclist + the distance traveled by the car = the total distance.

19r = 646 + 9.5*33.4

I will leave the arithmetic to you!