Puzzle Details

My bath has two taps and a plug hole - and a leak!

The cold tap on its own fills the bath in 20 minutes, the hot one in 30 minutes.

The plug hole can drain the bath in 16 minutes with the taps off.

The leak would empty a full bath in 2 hours.

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

In 24 hours:

- the cold tap could fill 72 baths
- the hot tap could fill 48 baths
- the plug could drain 90 baths
- the leak could drain 12 baths

Therefore, in 24 hours, we have 72 + 48 - 90 - 12 baths full = 18 baths.

Therefore each bath would take 80 minutes to fill.

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