Two taps can fill a tub in 6 minutes and 4 minutes, respectively. A pipe can empty it in 3 minutes. If all the three are kept open simultaneously, when will the tub be full?
12 min
Work the rates in "tub per minute". The first tap fills \(\dfrac{1}{6}\) of the tub each minute and the second fills \(\dfrac{1}{4}\).
The emptying pipe removes \(\dfrac{1}{3}\) of the tub each minute, so it counts as negative.
Net rate with all three open \(= \dfrac{1}{6} + \dfrac{1}{4} - \dfrac{1}{3}\).
Taking LCM 12: \(= \dfrac{2}{12} + \dfrac{3}{12} - \dfrac{4}{12} = \dfrac{1}{12}\) tub per minute.
Time to fill \(= \dfrac{1}{\,1/12\,} = 12\) minutes.
Hence, the tub will be full in 12 minutes.
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