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?

Do not do any rounding.

Answer 1

After
`h` hours, the distance the runner went is

`4h`
and the distance the cyclist went is

`19(h-3)`

Set the two equations equal and solve for
`h`:

`4h=19(h-3)`

`\Rightarrow 4h=19h-57`

`\Rightarrow -15h=-57`

`\Rightarrow h=(57)/(15)`

`\Rightarrow h=(19)/(5)`

`\Rightarrow h=3.8`

The cyclist traveled
`h-3` hours, which is 0.8 hours