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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

122.0. "Monkey Business" by NY1MM::PINSLEY () Wed Aug 08 1984 13:33

This problem was shown to me by someone at digital.  It was submitted to
a publication by Douglas Williams (I am not sure of the publication).

A rope is hung over a fence so that an equal length hangs down on both sides.
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 widget that weighs exactly
the same as 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 his mother are 30 years.  The weight of the
banana plus one-half the weight of the monkey is one-fourth as much as the
sum of the combined weights of the widget and the rope.  The monkey's mother
is one-half as old as the monkey will be when he is three times as old as his
mother was when she was one-half as old as the monkey will be when he's twice
as old as he is now.

How long is the banana?
T.RTitleUserPersonal
Name		DateLines
122.1HARE::STANFri Aug 10 1984 02:053
This classic problem was submitted by Douglas Williams to the DEC
publication "Systems and Clusters Engineering News" (as filler)
and appeared on page 5 of the June 1984 issue (issue #140).
122.2How ripe is the banana?ZFC::DERAMODaniel V. D'Eramo, VAX LISP developerWed Jun 22 1988 12:1172
     Spoiler follows:
     
     
     Let

L = length of rope (inches)
D = density of rope (ounces per inch)
     D = 1/3 (pounds per foot) * 16 (ounces per pound) * 1/12 (feet per inch)
     D = 4/9
W = weight of monkey (ounces) = weight of widget (ounces)
d = density of banana (ounces per inch)
     d = 2
A = age of monkey (years)
     L/12 = A
M = age of monkey's mother (years)
     W = M
     A + M = 30
l = length of banana (inches)
     ld + W/2 = (W + LD)/4
T = twice the monkey's age (years)
     T = 2A
U = monkey's mother's age when she was one-half as old as ...
     U = T/2
V = monkey's age when he is three times as old as his mother was ...
     V = 3U
     M = V/2

     So we must solve for l in:

     D = 4/9
     d = 2
     L/12 = A
     W = M
     A + M = 30
     ld + W/2 = (W + LD)/4
     T = 2A
     U = T/2
     V = 3U
     M = V/2

Try to express each variable in terms of A:

     L = 12A
     T = 2A
     U = T/2 = A
     V = 3U = 3A
     M = V/2 = 3A/2
     W = M = 3A/2

     Now solve for A:

     A + M = 30
     A + 3A/2 = 30
     5A/2 = 30
     A = 12

     Now solve for l:

     L = 12A = 144
     W = 3A/2 = 18

     ld + W/2 = (W + LD)/4
     2l + 18/2 = (18 + (4/9)144)/4
     2l + 9 = 20 1/2
     2l = 11 1/2
     l = ...
    
     l = 5 3/4

     The banana is 5 3/4 inches long.

     Dan
122.3This appeared just a couple of months ago in "Parade" magazineSEURAT::NEWMANChuck Newman, 297-5499, MRO4-1/H16, Pole J13Thu Sep 06 1990 12:251
It was in the "Ask Marilyn" column.