Inflow - outflow

The tank will fill by inflow for 56 minutes and empties by outflow for 77 minutes.

How long does it take to fill the tank if it is open to inflow and outflow?

Final Answer:

x =  205.33 min

Step-by-step explanation:

$$\begin{gathered} t_1=56\text{min} \\ {t}_2=77\text{min} \\ x\cdot (\frac{1}{t_1}-\frac{1}{t_2})=1 \\ \frac{1}{x}=\frac{1}{t_1}-\frac{1}{t_2} \\ x=\frac{1}{1/t_1-1/t_2}=\frac{1}{1/56-1/77}=\frac{616}{3}\text{min}=205.33\text{min} \end{gathered}$$

Try another example