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?

(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.