Tank filling

The water tank is filled with the first inflow in 1 hour 20 minutes, the second in 60 minutes. How many minutes will the tank be half full with both inlets if the other inlet is opened 12 minutes later?

Final Answer:

x =  24 min

Step-by-step explanation:

$$\begin{gathered} a=1\cdot 60+20=80\text{min} \\ b=60\text{min} \\ \frac{1}{a}\cdot x+\frac{1}{b}\cdot (x-12)=\frac{1}{2} \\ \frac{1}{80}\cdot x+\frac{1}{60}\cdot (x-12)=\frac{1}{2} \\ 1/80\cdot x+1/60\cdot (x-12)=1/2 \\ 7x=168 \\ x=\frac{168}{7}=24 \\ x=24=24\text{min} \end{gathered}$$

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