Suppose that a cyclist began a 532 mile ride across a state at the western edge

Question

Suppose that a cyclist began a 532 mile 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 9.5hours and the car traveled 37.6 mph faster than the bicycle find the average rate of each Suppose that a cyclist began a 532 mile 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 9.5hours and the car traveled 37.6 mph faster than the bicycle find the average rate of each

Explanation / Answer

Let the average speed of bicycle be x mph
then average rate of car is (x+37.6) mph

Net speed when both are moving towards each other,
vnet = x + (x+37.6)
= 2x + 37.6

Now use:
net distance = vnet * time
532 miles = (2x + 37.6)mph * 9.5 h
532 = 19x + 357.2
19x = 532 - 357.2
19x = 174.8
x = 174.8/19
= 9.2

Answer:
bicycle : 9.2 mph
car: 9.2+37.6 = 46.8 mph

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