Answer:
7 1/2 minutes
Step-by-step explanation:
When the time with both faucets is a submultiple of the time with one faucet, you can use this sort of reasoning to figure the missing time.
Filling the tub in 5 minutes is equivalent to having 3 faucets open, each of which can fill the tub in 15 minutes. Since we know the cold water faucet can fill the tub in 15 minutes, the hot water faucet is equivalent to two open 15-minute faucets. That is, it can fill the tub in 15/2 = 7 1/2 minutes.
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Perhaps a more conventional way to approach the problem is to consider "tubs per minute." The cold faucet runs at 1/15 tubs per minute, and the two faucets together run at 1/5 tub per minute. Then the hot runs at ...
(1/5) - (1/15) = (3 -1)/15 = 2/15 . . . tubs per minute
So it will fill 2 tubs in 15 minutes, or 1 tub in 7 1/2 minutes.
