Tank 28

A tank fills in 120 hours. When drained for irrigation, it empties in 10 days. How long will it take to fill if filling and draining occur simultaneously?

Final Answer:

t =  240 h

Step-by-step explanation:

$$\begin{gathered} t_1=120\text{h} \\ {t}_2=10\cdot 24=240\text{h} \\ t\cdot (\frac{1}{t_1}-\frac{1}{t_2})=1 \\ h=\frac{1}{t_1}-\frac{1}{t_2}=\frac{1}{120}-\frac{1}{240}=\frac{2}{240}-\frac{1}{240}=\frac{2-1}{240}=\frac{1}{240}\doteq 0.00421\text{/h} \\ t\cdot h=1 \\ t=1/h=1/0.0042=240\text{h} \end{gathered}$$

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