Along 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?

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.

0 is its x and y coordinate

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step-by-step explanation: