Bath filling

It happens to Dorothy that when filling the bath with water, she forgets to put a plug in the drain. The bath would fill up in 20 minutes if the drain were blocked. A full tub would be emptied through the drain in 30 minutes. How long will it take Dorothy to fill the bathtub if she forgets to plug the drain?

Final Answer:

t =  60 min

Step-by-step explanation:

$$\begin{gathered} a=20\text{min} \\ b=30\text{min} \\ Q=\frac{1}{a}-\frac{1}{b}=\frac{1}{20}-\frac{1}{30}=\frac{3}{60}-\frac{2}{60}=\frac{3-2}{60}=\frac{1}{60}\doteq 0.0167 \\ Q\cdot t=1 \\ t=1/Q=1/0.0167=60\text{min} \end{gathered}$$

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