Henry Ernest Dudeney/Modern Puzzles/188 - Monkey and Pulley/Solution

by : $188$

 * Monkey and Pulley

Solution

 * $5$ feet.

Proof
First recall that there are $16$ ounces to the pound.

All weights will be discussed hereforth in ounces.

Let $l$ feet be the length of the rope.

Let $m$ years be the age of the monkey.

Let $n$ years be the age of the monkey's mother.

Let $w$ be the weight of the rope.

Let $x$ be the weight of the monkey.

Let $y$ be the weight of the weight.

Let $a$ be the number of years ago when the monkey's mother was $3$ times as old as the monkey.

Let $b$ be the number of years ahead when the monkey will be $3$ times as old as the monkey's mother was at $a$.

Let $c$ be the number of years ago when the monkey's mother was half as old as the monkey will be at $b$.

Now we proceed.

Starting near the bottom and working our way up, we whittle down the variables: