solving a distance, rate, time problem using a linear funtion

Question

A long distance runner starts at the beginning of a trail and runs at a rate of
4
miles per hour. Three hours later, a cyclist starts at the beginning of the trail and travels at a rate of
19
miles per hour. What is the amount of time that the cyclist travels before overtaking the runner?

Answer 1

runner covers distance = 4t in t hours

cyclist covers same distance in 19(t-3) hours.

Set these two quantities equal; solve for t