Filling a pool with the drain open

MediumBrainteasers~4m

One hose fills a kiddie pool in $20$ minutes; another fills it in $10$ minutes. An open drain empties a full pool in $15$ minutes. With both hoses running and the drain open, how many minutes does it take to fill the empty pool?

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Work in rates (pools/min): $\tfrac1{20}+\tfrac1{10}-\tfrac1{15}$ .
Net $=\tfrac1{12}$ , so $12$ minutes.

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Filling a pool with the drain open

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