Three taps A, B and C together can fill a tank in 6 hours. Tap C alone can fill the tank in 12 hours. To fill the tank, when it is empty, <strong>ALL</strong> the three taps are started together. After working t hours, tap C is closed and the tank is filled in 8 more hours. What is t equal to?

Explanation

The combined rate of A, B, and C is \frac{1}{6}, and C alone is \frac{1}{12}. The combined rate of A and B is \frac{1}{6} - \frac{1}{12} = \frac{1}{12}. For total work: t(\frac{1}{6}) + 8(\frac{1}{12}) = 1 \implies \frac{t}{6} + \frac{2}{3} = 1 \implies \frac{t}{6} = \frac{1}{3} \implies t=2.

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