Water reservoir

The water reservoir is filled with one pump for four days by the second one for nine days. An outlet can drain the tank in 12 days. How long does it take to fill the reservoir if both pumps are running and not closed outlet channels?

Correct answer:

t =  3.6 d

Step-by-step explanation:

$$\begin{gathered} Q=\frac{1}{4}+\frac{1}{9}-\frac{1}{12}=\frac{9}{36}+\frac{4}{36}-\frac{3}{36}=\frac{9+4-3}{36}=\frac{10}{36}=\frac{5}{18}\doteq 0.2778 \\ t\cdot Q=1 \\ t=1/Q=1/\frac{5}{18}=1:\frac{5}{18}=1\cdot \frac{18}{5}=\frac{1\cdot 18}{5}=\frac{18}{5}=\frac{18}{5}\text{d}=3.6\text{d} \end{gathered}$$

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