Two pipes $P$ and $Q$ fill a cistern in 24 and 32 minutes respectively. Both pipes are kept open. When should the first pipe be turned off so that the cistern may be just filled in 16 minutes?

Using the work proportion method, pipe P fills one twenty-fourth of the cistern per minute and pipe Q fills one thirty-second per minute. Over the sixteen minutes it takes to fill the cistern, pipe Q contributes sixteen divided by thirty-two, which is exactly half the tank. This leaves the remaining half of the cistern to be filled by pipe P. Since pipe P fills one twenty-fourth per minute, dividing one half by one twenty-fourth gives the time pipe P must stay open as twelve minutes.

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