Suppose that a cyclist began a 374 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 5.5 hr and the car traveled 33.433.4 mph faster than the bicycle, find the average rate of each.

This is the concept of relative speed; We are required to calculate the speed of the car and the bicycle.

Distance between the car and Bicycle=374 miles

Time they met=5.5 hr

Speed traveled by bicycle=x

Speed traveled by car=x+33.4334

Relative speed=x + (x+33.4334) = (2x+33.4334) mph

Distance=speed*time

374 = (2x+33.4334) * 5.5

374=11x+183.8837

collecting like term we get:

374-183.8837=11x

11x=190.1163

thus;

x = (190.1163) / (11)

x=17.2833 mph

thus the speed of the bicycle was x=17.2833 mph

The speed of the car was (x+33.4334) = (17.2833+33.4334) = 50.7167 mph