Suppose that a cyclist began a 570 mi ride across a state at

Suppose that a cyclist began a 570 mi ride across a state at the western edge of the state, at the same time that a car traveling toward it leaves the easters and of the state. If the bicycle and car met after 9.5 hr and the car traveled 37.6 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.

Solution

Let rate = the rate (speed) of the bicyclist.

Since the car went 37.6 mph faster than the bike, its speed = rate + 37.6.

distance = rate*time

570 miles = rate*(9.5 hours) + (rate+37.6 mph)*(9.5 hours)

=> 570 = 9.5*rate + 9.5*rate + 357.2

=> 570 - 357.2 = 19*rate

=> 11.2 mph = rate (of the bike)

rate of the car = 11.2+37.6 = 48.8 mph