Along distance runner starts at the beginning of a trail and runs at a rate of 5 miles per hour. one hour later, a cyclist starts at the beginning of the trail and travels at a rate of 13 miles per hour. what is the amount of time that the cyclist travels before overtaking the runner?

my answer is 37.5 minutes but it has to be in where am i going wrong?

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.