My Favorite Math Problem

Math has never been my passion; in fact, excepting geometry--which captivated me with its "proofs"--I reluctantly approached every math class I ever had. I have to admit, however, that I have used math regularly in my life, and those tedious sessions learning how to understand numbers were not wasted. Nonetheless, it was language and the puzzle of it that first attracted me to this particular problem. I actually thought the problem was a spoof when I first heard it, back in my high school days, so I didn't try to solve it. Instead, I scrawled it, word for word, into a tiny diary which I acquired and maintained somewhere around my senior year, and saved throughout the years to remind myself not to be too hard on my high school students when they seem immature. Some years later, I happened to run across this problem while shaking my head over the diary and its inane contents, and I discovered that it actually was a valid puzzle. I labored as only a non-math person can labor over math, and finally solved it. Thereupon I declared it my favorite math problem and have challenged students with it for years, keeping a list of those who managed to solve it. If you find the answer (without help...be honest now) send me your answer at lilibethsblog@gmail.com and I will affix a list of "those who got it right" on this post. I wish I had a huge prize to offer, but I don't. Blog fame will have to suffice. Here is the problem:

Over the top of the fence is placed a rope, the same amount on both sides. The rope weighs 1/3 pound per foot. On one end of the rope hangs a monkey with a banana, and on the other end hangs a weight equal in weight to 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 its mother are thirty years. The weight of the banana plus 1/2 the weight of the monkey is 1/4 th as much as the sum of the weights of the weight and the rope, where all weights are in the same unit. The monkey's mother is 1/2 as old as the monkey will be when it is three times as old as its mother was when she was 1/2 as old as the monkey will be when it is twice as old as it is now.

Question: How long is the banana?

Students who have solved this: Patrick S, Kenny P, Matthew E, Carolyn T, Roman R, Erin F, Corey H, Kent Mc.