Graduate Level Math Word Problem

You know how they say “Last one is the best?” Well, here is the graduate level word problem:

A rope is hung over a fence so that an equal length hangs down on both sides. The rope weighs one-third pound per foot. On one end of the rope hangs a monkey holding a banana, and on the other end is a widget that weighs exactly the same as the monkey. The banana weighs two ounces per inch. The length of the rope, in feet, is equal to the age of the monkey. 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 his mother are 30 years. The weight of the banana plus one-half the weight of the monkey is one-fourth as much as the sum of the combined weights of the widget and the rope. The monkey’s mother is one-half as old as the monkey will be when he is three times as old as his mother was when she was one-half as old as the monkey will be when he’s twice as old as he is now.

How long is the banana?

Consider yourself an honorary algebra wizard if you can get this, but ya gotta show your work for full credit…