Originally written this way for my children, now
it is your challenge!
This Is Not a Trick Question
The first one of my childeren to solve this problem and from whom I receive an acceptably delineated and executed solution with the exact right answer will be awarded (unless he is a "brain", in which case he should be willing to accept $50 because it isn't right to take advantage of Dad). No consultation or help is allowed (other than prayer)!
When I was in high school, I dated a girl whose father was something of a math genius by reputation. One day he sat me down and said, "Neal, I hear your are a bright chap!". (The family had come from England, and so the word "chap" was normal colloquoy under the circumstances.) Probably more from wanting to appear appropriately humble and not to be trapped than from honesty, I restrained myself from blurting out something like, "Right on old chap!". Instead I sort of hemmed and hawed with body language and appropriate grunts and self-effacements to say that yes I was bright, but was not a braggert, yet all designed to convey that I really was exceptional.
I must have convinced this father, because through his daughter he gave me this following problem to see if I could solve it and obtain the right answer. I did. Can you?
1.) Over the top of a fence there is placed a rope, the same amount on both sides. The rope weighs 1/3 lb. 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.
2.) The banana weighs two ounces/inch. The length of the rope (in feet) is as long as 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. The combined ages of the monkey and its mother is 30 years.
3.) 1/2 the weight of the monkey plus the weight of the banana is 1/4 as much the weight of the total rope and the weight.
4.) The monkey's mother is 1/2 as old as the monkey will be when it is 3 times as old as its mother was when she was 1/2 as old as the monkey will be when it is as old as its mother will be when she is 4 times as old as the monkey was when it was twice as old as its mother was when she was 1/3 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 1/4 as old as it is now.
5.)How long is the banana?