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

by : $188$

 * Monkey and Pulley
 * Here is a funny tangle.
 * It is a mixture of 's "Monkey and Pulley", 's "How old was Mary?" and some other trifles.
 * But it is quite easy if you have a pretty clear head.


 * A rope is passed over a pulley.
 * It has a weight at one end and a monkey at the other.
 * There is the same length of rope on either side and equilibrium is maintained.
 * The rope weighs four ounces per foot.
 * The age of the monkey and the age of the monkey's mother total four years.
 * The weight of the monkey is as many pounds as the monkey's mother is years old.
 * The monkey's mother is twice as old as the monkey was
 * when the monkey's mother was half as old as the monkey will be
 * when the monkey is three times as old as the monkey's mother was
 * when the monkey's mother was three times as old as the monkey.
 * The weight of the rope and the weight at the end was half as much again as the difference in weight
 * between the weight of the weight and the weight of the monkey.
 * Now, what was the length of the rope?