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Fat Cats (Posted on 2002-05-14) Difficulty: 2 of 5
Three fat cats can eat three fat rats in three minutes. How long will it take for thirty three fat cats to eat sixty six fat rats?

See The Solution Submitted by levik    
Rating: 2.4286 (14 votes)

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Solution Puzzle Solution: Method II | Comment 18 of 20 |
(In reply to Puzzle Solution by K Sengupta)

In the given problem, we say "P a Q" for "P varies as Q"

If X fat cats consume Y fat rats in Z minutes, then for fixed Z, we
must have X a Y. Similarly, for fixed Y, it follows that X a 1/Z.

Thus, X*Z/Y = a constant.

Thus, for two sets of triples (X_1, Y_1, Z_1) and (X_2, Y_2, Z_2), we must have:

X_1*Z_1/Y_1 = X_2*Z_2/Y_2

By the given conditions, (X_1, Y_1, Z_1) = (3,3,3) and :
(X_2, Y_2) = (33, 66), and accordingly:

(3*3)/3 = (66/33)*Z_2, giving:

Z_2 = 6

Consequently, it will take six minutes for thirty three fat cats
to eat sixty six fat rats.

  Posted by K Sengupta on 2008-05-13 05:55:37
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