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The Monkey and the Banana

A rope is placed over the top of a fence, the same amount of rope on both sides of the fence. 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 weight equal in weight to the weight of the monkey.

The banana weighs two ounces per inch. The length of the rope (in feet) is equal to the age of the monkey (in years), and the weight of the monkey (in ounces) is as much as the age of the monkey's mother (in years). The combined ages of the monkey and its mother are thirty years.

The weight of the banana plus half of the weight of the monkey is one-fourth as much as the sum of the weights of the weight of the rope, where all weights are in the same units.

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 twice as old as it is now.

How long is the banana?

If you can answer that, you don't belong in Honors. You belong on the moon. The Alfred University Honors Program "official" answer, by the way, is six and seven eighths inches. All bananas, as far as we can tell, are six and seven eighths inches long.