Question

A long distance runner starts at the beginning of a trail and runs at a rate of
4 miles per hour. Two hours later, a cyclist starts at the beginning of the trail and travels at a rate of 14 miles per hour. What is the amount of time that the cyclist travels before overtaking the runner?

Do not do any rounding.

Answer 1

Hello!

When the cyclist starts,the runner will have already ran 8 miles. We can write this equation below, where h represents the hours run since the cyclist took off.

14h=8+4h

Let's move the variables onto one side. First we subtract 4h from both sides.

10h=8

Now we divide both sides by 8.

1.25

As you can see, it will take 1.25 hours for the cyclist to overtake the runner.

I hope this helps!