A rope over the top of a pulley
has the same length on each side. It weighs one third of a pound per foot. On
one end hangs a monkey holding a banana, and on the other end is attached a
weight equal to the weight of the monkey and the banana. The banana weighs two
ounces per inch. The rope is as long (in feet) as the age of the monkey (in
years), and the weight of the monkey (in ounces) is the same as the age of the
monkey's mother.

The combined ages of the monkey
and its mother are thirty years. One half the weight of the monkey, plus the
weight of the banana, is one fourth as much as the weight of the weight and the
weight of the rope. The monkey's mother is half as old as the monkey will be
when it is three times as old as its mother was when she was 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?