Answer to Problem of the Week for 3/29/99

Answer to March 29, 1999 Problem

The Banana Problem
A rope over the top of a fence has the same length on each side, and weighs one-third of a pound per foot. On one end hangs a monkey holding a banana, and on the other end a weight equal to the weight of the monkey. The banana weighs 2 ounces per inch. The length of the rope in feet is the same as the age of the monkey, and the weight of the monkey in ounces is as much as the age of the monkey's mother. The combined ages of the monkey and its mother are 30 years. One-half the weight of the monkey, plus the weight of the banana is one-fourth the sum of the weights of the rope and the weight. The monkey's mother is one-half as old as the monkey will be when it is three times as old as its mother was when she was one-half as old as the monkey will be when it is as old as its mother will be when she is four times as old as the monkey was when it was twice as old as its mother was when she was one-third as old as the monkey was when it was as old as its mother was when she was three times as old as the monkey was when it was one-fourth as old as it is now. How long is the banana?

The Banana Problem

A rope over the top of a fence has the same length on each side, and weighs one-third of a pound per foot. On one end hangs a monkey holding a banana, and on the other end a weight equal to the weight of the monkey. The banana weighs 2 ounces per inch. The length of the rope in feet is the same as the age of the monkey, and the weight of the monkey in ounces is as much as the age of the monkey's mother. The combined ages of the monkey and its mother are 30 years. One-half the weight of the monkey, plus the weight of the banana is one-fourth the sum of the weights of the rope and the weight. The monkey's mother is one-half as old as the monkey will be when it is three times as old as its mother was when she was one-half as old as the monkey will be when it is as old as its mother will be when she is four times as old as the monkey was when it was twice as old as its mother was when she was one-third as old as the monkey was when it was as old as its mother was when she was three times as old as the monkey was when it was one-fourth as old as it is now. How long is the banana?

Solution:

The answer is 5.75 inches long.

Let A = age of the monkey now and
let M = age of his Mother.
Then A + M = 30.
From the long sentence,
M = .5(3(.5(4(2((1/3)(3(.25A))))))
Solving simultaneously, 2.5 A = 30
so A = 12 (the age of the monkey) and
M = 18 (the age of the monkey's mother).

So the weight of the monkey is 18 oz.
The length of the rope is 12 feet.
The rope weighs 2 pounds.
The weight weighs 18 ounces.
The banana weighs 11.5 ounces, so
the banana is 5.75 inches long.

Correctly solved by:

1. Ginger Anderson	Winchester, VA
2. Dave Manning	Coopersburg, PA (Lehigh University)

Answer to March 29, 1999 Problem

Correctly solved by: