Inlet minus outlet

Water flows into the tank through two pipes and out of the third pipe spontaneously. Pipe A would fill the tank in 3 hours, pipe B would fill in 4 hours, and pipe C would flow out in 12 hours. If all three pipes open simultaneously, how long will the tank be full?

Correct answer:

t =  2 h

Step-by-step explanation:

$$\begin{gathered} Q=\frac{1}{3}+\frac{1}{4}-\frac{1}{12}=\frac{4}{12}+\frac{3}{12}-\frac{1}{12}=\frac{4+3-1}{12}=\frac{6}{12}=\frac{1}{2}=0.5 \\ t\cdot Q=1 \\ t=\frac{1}{Q}=\frac{1}{0.5}=2\text{h} \end{gathered}$$

Try another example