The Bathtub

A bathtub is filled by running water from both the hot and cold taps.
The hot tap alone takes 6 minutes to fill the tub.
The cold tap alone takes 4 minutes to fill the tub.
An open drain plug empties the tub in 12 minutes.
Both taps are fully open at the same time, while the drain plug is accidentally left out.
How long will it take to fill the tub?

Solution

 

In 1 minute, 
the hot tap fills 1/4 of the tub,
the cold tap fills 1/3 of the tub,  
the drain plug drains 1/12 of the tub.

The net gain in 1 minute is 1/6 + 1/4 - 1/12 
= 2/12 + 3/12 - 1/12 
= 4/12
= 1/3 of tub

Therefore, it takes 3 minutes to fill the bath.