Answer: a long distance runner starts at the beginning of a trail and runs at a rate of 4 miles per hour. one hour later, a cyclist starts at the beginning of the trail and travels at a rate of 20 miles per hour. what is the amount of time that the cyclist travels before overtaking the runner?

Let t = travel time of the cyclist

then,

(t+1) = travel time of the runner (he start 1 hr before the cyclist)

When the cyclist overtakes the runner, they will have traveled the same distance

Write a distance equation: dist = speed * time

Cyclist dist = runner's dist

20t = 4 * (t+1)

20t = 4t+4

20t-4t = 4

16t = 4

t = 4/16 = 1/4

t = 1/4 hr for the cyclist to catch the runner

The amount of time that the cyclist travels before overtaking the runner = 1/4 hr or 15 minutes