Question

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?

Answer 1

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.