The original puzzle
The cold water tap, completely opened, fills the bath in 3 minutes.The hot water tap, completely opened, fills the bath in
4 minutes. When the plug is removed, the bath empties in 12 minutes. How long will it take to fill the bath with both taps
open and the plug removed ?
Here one must work with the amount of water in the bath
and not the number of minutes it takes to fill it.
In 1 minute,
the cold water tap will fill 1/3 of the bath,
the hot water tap will fill 1/4 of the bath, and
the drain will remove 1/12 of the bath,
with a cumulative result of 1/3 + 1/4 - 1/12 = 6/12, or 1/2 of the bath.
It will take two minutes flat to fill the bath !