Question

On a hike up hill, Ted climbs at 3 miles an hour. Going back down, he runs at 5 miles an hour. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike?

Answer 1

The length of hike is 5 miles.

Step-by-step explanation

Suppose, the length of the hike is
`x` miles.

On a hike up hill, Ted climbs at 3 miles an hour and going back down, he runs at 5 miles an hour.

We know that,
`Time= (Distance)/(Speed)`

So, the time taken by him to climb up
`= (x)/(3)` hours and the time taken by him to run down
`= (x)/(5)` hours.

Given that, it takes him 40 minutes longer to climb up than run down. Now, 40 minutes
`=(40)/(60)hours=(2)/(3)` hours.

So the equation will be......

`(x)/(3)-(x)/(5)=(2)/(3)\\ \\ 15((x)/(3)-(x)/(5))=15((2)/(3))\\ \\ 5x-3x=10\\ \\ 2x=10\\ \\ x=5`

So, the length of hike is 5 miles.