Suppose that a cyclist began a 527 mi ride across a state at the western edge of the? state

Question

Suppose that a cyclist began a 527 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 30.8 mph faster than the? bicycle, find the average rate of each.

Answer 1

Let rate = the rate (speed) of the bicyclist.  Since the car went 30.8 mph faster than the bike, its speed = rate + 30.8.

 

distance = rate*time

 

527 miles = rate*(8.5 hours) + (rate+30.8 mph)*(8.5 hours)

 

527 = 8.5*rate + 8.5*rate + 261.8

 

265.2 = 17*rate

 

15.6 mph = rate (of the bike)

 

rate of the car = 15.6 + 30.8 = 46.4 mph