Two pipes P and Q can fill a tub in 20 minutes and 30 minutes, respectively. If both the pipes are opened simultaneously, then after how many minutes should pipe P be turned off, so that the tub is filled in exactly 15 minutes?

Using the one-day work method, pipe Q works for the full 15 minutes at a rate of 1/30 per minute, contributing 15/30 or 1/2 of the tub. Pipe P must supply the remaining 1/2 of the tub at its rate of 1/20 per minute. The time pipe P needs to be open is (1/2) / (1/20) = 10 minutes, so it should be turned off after 10 minutes.

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