Solving a distance, rate, time problem using a linear equation

Question

A long 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?

 

No rounding.

Answer 1

let cyclist travel x hour

since runner started 1 hr earlier he travels (x+1) hr

 

but since he overtakes him distances coverd by both is same 

 

distance=speed * time

 

so x*13=5*(x+1)

x=5/8 hr =37.5 min