My bath has two taps and a plug hole. The cold tap on its own fills the bath in 12 minutes, the hot one in 8 minutes. The plug hole can drain the bath in 24 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, the cold tap could fill 120 baths, the hot tap could fill 180 baths and the plug could drain 60 baths.
Therefore, in 24 hours, we have 120 + 180 - 60 baths full = 240 baths.
Therefore each bath would take 6 minutes to fill.