SOME MONKEY BUSINESS: Hanging over a pulley is a rope. At one end of the rope is a sand bag and at the other end is a monkey. The weight of the monkey is the same as the weight of the sand bag. The rope weighs 4 ounces per foot.
The sum of the ages of the monkey and the monkey's mother is 4 years. The monkey's weight in pounds is the same as the mother's age in years.
The mother is twice as old as the monkey was when the mother was half as old as the monkey will be when the monkey is three times as old as the mother was when she was three times as old as the monkey was.
The weight of the rope and the sand bag is one and a half times the weight of the monkey. How long is the rope?
[Problem submitted by Roger Wolf, LACC Professor of Mathematics and Chairman of the Department of Mathematics and Computer Science.]