A troop of scots hiked to the county scout cabin at the rate of 2 miles per hour. They rode back to headquarters at 18 miles per hour. If the round trip took 10 hours, how far is headquarters from the cabin?

Question

watchmath · Answer

Let $x,y$ be the times needed to go up and down respectively. Then $x+y=10$ and $\text{distance}=2x=18y$. So $x=9y$ and hence $10y=10$. So $y=1$ and $x=9$. So the distance of the headquarter from the cabin is $2x=18$ miles.