The dam

The water reservoir is filled with the first tributary for 25 hours and the second tributary for 35 hours. Sometimes, both inlets open, then a second tributary closed, and they filled the tank in four hours. What time does water flow from both tributaries? (Expressed in hours and minutes)

Result

t = 12:55 hh:mm

Step-by-step explanation:

$$\begin{gathered} a=25\text{h} \\ b=35\text{h} \\ \frac{1}{a}\cdot t+\frac{1}{b}\cdot (t+4)=1 \\ \frac{1}{25}\cdot t+\frac{1}{35}\cdot (t+4)=1 \\ 1/25\cdot t+1/35\cdot (t+4)=1 \\ 12t=155 \\ t=\frac{155}{12}=12.91666667 \\ t=\frac{155}{12}\doteq 12.916667=12.91667=12:55\text{hh}:\text{mm} \end{gathered}$$

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