Over the top of a fence hangs a rope. On one end of the rope a monkey is holding a banana. On the other end of the rope hangs a weight equal to the weight of the monkey. The rope weighs one third pounds per foot and the banana weighs two ounces per inch. The length of the rope in feet is the same as the age of the monkey. The weight of the monkey in ounces is the same as the age of the monkey's mother in years. The combined ages of the monkey and its mother are thirty years.

One half the weight of the monkey plus the the weight of the banana is a quarter as much as 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 a 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 a quarter as old as it is now.

How long is the banana?