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Monkey on a rope

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A rope over the top of a fence has the same length on each side and weighs one-third of a pound per foot. On one end hangs a monkey holding a banana, and on the other end a weight equal to the weight of the monkey. The banana weighs 2 ounces per inch. The length of the rope in feet is the same as the age of the monkey, and the weight of the monkey in ounces is as much as the age of the monkeys mother. The combined ages of the monkey and its mother are 30 years. One-half the weight of the monkey plus the weight of the banana is one-fourth the sum of the weights of the rope and the weight. The monkeys mother is one half as old as the monkey will be when it is three times as old as its mother was when she was one 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?

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Posted · Report post

5 3/4 in. The algebra is straightforward enough that I won't show the details. Just took brute force reading through the clues.

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Posted · Report post

Has a familiar ring. Glad it got stated clearly this time and the solution was found. ;)

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