Question

Suppose that a cyclist began a 364 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 6.5 hr and the car traveled 31.4 mph faster than the​ bicycle, find the average rate of each. The​ car's average rate is ___ mph. The​ bicycle's average rate is ___ mph. ​(Type an integer or a​ decimal.)

Answer 1

The car's average rate  is 43.7 mph. The bicycle's average rate is 12.3 mph.

To get this solution, let the bicycle's average rate be (x) and the car's average rate be (x + 31.4) mph. 

Distance= Speed x Time
364 = (x + x + 31.4) 6.5
364 = (2x + 31.4) 6.5
364/6.5 = 2x + 31.4
56 = 2x + 31.4
56 - 31.4 = 2x
24.6 = 2x
24.6/2 = x
12.3 = x

x = 12.3 mph     
x+31.4 = 43.7 mph