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?