A long distance runner starts at the beginning of a trail and runs at a rate of
5
miles per hour. Two hours later, a cyclist starts at the beginning of the trail and travels at a rate of
9
miles per hour. What is the amount of time that the cyclist travels before overtaking the runner?

Question

A long distance runner starts at the beginning of a trail and runs at a rate of 
5
 miles per hour. Two hours later, a cyclist starts at the beginning of the trail and travels at a rate of 
9
 miles per hour. What is the amount of time that the cyclist travels before overtaking the runner?

anonymous · Answer

Equate the two velocities:
$$5x + 10 = 9x$$
Solve for x:
$$x = \frac{ 5 }{ 2 } = 2.5$$
So after 2.5 hours, the cyclists would've overtaken the runner.