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Puzzle Details

My bath has two taps and a plug hole.

The cold tap on its own fills the bath in 18 minutes, the hot one in 9 minutes.

The plug hole can drain the bath in 15 minutes with the taps off.

How long will the bath take to fill if I leave both taps on with the plug left out?

In 24 hours there are 1,440 minutes.

So, in 24 hours the cold tap can fill 1440 ÷ 18 = 80 baths.

Also, in 24 hours the hot tap can fill 1440 ÷ 9 = 160 baths.

Finally, in 24 hours the plug hole can empty 1440 ÷ 15 = 96 baths.

So, in 24 hours we have 80 + 160 - 96 = 144 baths. So each bath would take 1440 ÷ 144 = 10 minutes to fill.

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