Henry Ernest Dudeney/Modern Puzzles/28 - Hill Climbing

by : $28$

 * Hill Climbing
 * Weary Willie went up a certain hill at the rate of $1 \tfrac 1 2$ miles per hour
 * and came down at the rate of $4 \tfrac 1 2$ miles per hour,
 * so that it took him just $6$ hours to make the double journey.


 * Now, how far was it to the top of the hill?

Solution

 * $6 \tfrac 3 4$ miles.

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: