Continuous filling and filling

Okay, so we must determine the rate of accumulation of water in the tank. For this, we must find the flow rates of both taps, as well as the flow rate of the drain:

Tap A: $fr_{A} = \frac{V}{20}$

Tap B: $fr_{B} = \frac{V}{30}$

Drain: $fr_{Dr} = -\frac{V}{50}$ (Here the minus sign indicates that water is being taken from the system.)

The rate of accumulation of water will then be the sum of the flow rates:

$fr_{global} = fr_{A} + fr_{B} + fr_{Dr} = \frac{V}{20} + \frac{V}{30} - \frac{V}{50} = \frac{19V}{300}$ .

Thus, the rate of accumulation is $\frac{19V}{300}$ ; since it must equal the volume of the tank divided by the time taken to fill it, then we have:

$\frac{V}{t} = \frac{19V}{300} \rightarrow t = \frac{300}{19} \approx 15.79 min$