Question

Louisa ran at an average speed of five miles per hour along an entire circular park path. Calvin ran along the same path in the opposite direction at an average speed of six miles per hour. It took Calvin 30 minutes less than it took Louisa to run the full path once. How many miles did Louisa run when she completed one circular path?

Answer 1

15 miles

Explanation:

Let
`x` be the miles in the circular park path,
`t_(L)` the time Louisa takes to finish and
`t_(C)` the time Calvin takes to finish both in hours.

Then
`x`, the longitude is equal to the velocity times the time used to finish. So

`x=5t_(L)`

`x=6t_(C)`

And the difference between Louisa's time and Calvin' time is 30 minutes, half an hour. So:

`t_(C)=t_(L)-0.5`

Three equations, three unknowns, the system can be solved.

Equalizing the equation with x :

`5t_(L)=6t_(C)`

In this last equation replace
`t_(C)` with the other equation and solve:

`5t_(L)=6(t_(L)-0.5)\\ 5t_(L)=6t_(L)-3\\ 3=6t_(L)-5t_(L)\\ 3=t_(L)\\ t_(L)=3`

With Louisa's time find x:

`x=5t_(L)\\ x=5(3)\\ x=15`