Question

A long distance runner starts at the beginning of a trail and runs at a rate of 4 miles per hour. two hours later, a cyclist starts at the beginning of the trail and travels at a rate of 14 miles per hour. what is the amount of time that the cyclist travels before overtaking the runner?

Answer 1

To solve this problem, let us first assign variables. Let us say that:

A = runner

B = cyclist

d = distance

v = velocity

time = t

The time in which the cyclist overtakes the runner is the time wherein the distance of the two is the same, that is:

dA = dB

We know that the formula for calculating distance is:

d = v t

therefore,

vA tA = vB tB

Further, we know that tA = tB + 2, therefore:

vA (tB + 2) = vB tB

4 (tB + 2) = 14 tB

4 tB + 8 = 14 tB

10 tB = 8

tB = 0.8 hours = 48 min

Therefore the cyclist overtakes the runner after 0.8 hours or 48 minutes.