# A long distance runner starts at the beginning of a trail and runs at a rate of 5 miles per hour. Three hours later, a cyclist starts at the beginning of the trail and travels at a rate of 8 miles per hour. What is the amount of time that the cyclist travels before overtaking the runner? Do not do any rounding.

The long distance runner starts at the beginning of a trail and runs at a rate of 5 miles per hour. Three hours later, a cyclist starts at the beginning of the trail and travels at a rate of 8 miles per hour.

Let the cyclist overtake the runner after...

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The long distance runner starts at the beginning of a trail and runs at a rate of 5 miles per hour. Three hours later, a cyclist starts at the beginning of the trail and travels at a rate of 8 miles per hour.

Let the cyclist overtake the runner after T hours.

The distance traveled by the runner when the cyclist overtakes him is 5*(T + 3) and the distance traveled by the cyclist is T*8

Equating the two, 5T + 15 = 8T

=> 3T = 15

=> T = 5

The cyclist overtakes the runner after traveling for 3 hours.

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