A rope is placed over the top of afence, the same amount of rope on both sides p

Question

A rope is placed over the top of afence, the same amount of rope on both sides pf the fence. The ropeweighs one-third pound per foot.
On one end of the rope hangs a chimp holding a banana, and on theother end is a weight equal in weight to the chimp.
The banana weighs 2 ounces per inch. The length of the rope (infeet) is equal to the age of the chimp (in years), and the weightof the chimp (in ounces) is as much as the age of the chimp'smother (in years). The combined ages of the chimp and its mother is30 years.
The weight of the banana plus half the weight of the chimp isone-fourth as much as the sum of the weight of the rope, where theweights are in the same units.
The chimp's mother is half as old as the chimp will be when it isthree times as old as its mother was when she was half as old asthe chimp will be when it is twice as old as it is now.
How long is the banana? A rope is placed over the top of afence, the same amount of rope on both sides pf the fence. The ropeweighs one-third pound per foot.
On one end of the rope hangs a chimp holding a banana, and on theother end is a weight equal in weight to the chimp.
The banana weighs 2 ounces per inch. The length of the rope (infeet) is equal to the age of the chimp (in years), and the weightof the chimp (in ounces) is as much as the age of the chimp'smother (in years). The combined ages of the chimp and its mother is30 years.
The weight of the banana plus half the weight of the chimp isone-fourth as much as the sum of the weight of the rope, where theweights are in the same units.
The chimp's mother is half as old as the chimp will be when it isthree times as old as its mother was when she was half as old asthe chimp will be when it is twice as old as it is now.
How long is the banana?

Explanation / Answer

Wow. Convoluted question. Start at the bottom. Combined age of Chimp C and Mother M = 30 years. Saying "the mother's age when she was half as old as thechimp will be when it's twice as old as it is now" is an indirectway of saying "the chimp's age." 1/2 of 2C = C. So, we say that the Chimp's mother is half as old as the chimp willbe when it is three times as old as it is now. So, M = 1/2(3C). or M= 3/2 x C. Since M + C = 30, then we have C +(3/2 x C) = 30, or 5/2(C) = 30, or 5C = 60. ThereforeC = 12 years. Since M + 12 = 30, M = 18 years. Moving on, the weight of chimp C in oz (Cw) = the age of M, orCw = 18 oz The length of the rope R in feet (Rl) = the age of chimp C, orRl = 12 feet. The weight of the rope R in pounds (Rw) = 1/3 x length in feet, or1/3 x 12, or Rw = 4 pounds.Lastly, we have theweight of the banana (Bw) plus 1/2 x Cw = 1/4 x Rw. Bw = 1/4(Rw) - 1/2(Cw). Bw = 1/4(4lbs) - 1/2(18oz) Bw = 1 lb - 9oz Bw = 16oz - 9oz Bw = 7oz. Since the length of the Banana (Bl) = 2oz/inch, we have the lengthBl = 7oz/2oz, or Bl = 3.5 inches

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