A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?
A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?
Since we have 5 answers, first remove the two extremes and focus on the middle numbers. Let's go with (B) first. If Time (Drain) = 6, then Time (Q) = 2. Based on the fact that "with faucets P and Q both running and the drain unstopped, the tub fills in six minutes", you can deduce that with faucets P and Q both running, the tub should fill in 3 minues since they have to fill the tub twice as fast as the drain is letting go water. This is countrary to our presumption that Q only can fill the tub in 2 minutes. Wrong answer.
Let's try (C) second. If Time (Drain) = 10, then Time (Q) = 6. Since Time (Drain) = Time (P) = 10, then it means that these two cancel each other out and the time for Q alone should be the same as P, Q and D all together! Is it the case? Time (Q) = 6 = Time (P/Q/D) !
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发表于 2010-11-11 04:53:12
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