runner vs cyclist

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

let t be time of runner running

 

so,

 

4t = 19(t - 3)

 

4t = 19t - 57

 

4t - 19t = -57

 

-15t = -57

 

t = 3.8 hours

 

3.8 - 3 = .8 hours or 48 minutes