Henry Ernest Dudeney/Modern Puzzles/28 - Hill Climbing/Solution

by : $28$

 * Hill Climbing

Solution

 * $6 \tfrac 3 4$ miles.

He goes up in $4 \tfrac 1 2$ hours and back down again in $1 \tfrac 1 2$ hours.

Proof
Let $d$ miles be the distance to the top of the hill.

Let $t_1$ be the time taken to reach the top.

Let $t_2$ be the time taken to reach the bottom again.

The assumption has to be that no time is taken to rest at the top.

We have: