Two taps can fill a cistern in 4 hours and 20 hours, respectively. A third tap can empty it in 20 hours. How long (in hours) will it take to fill one-fourth of the empty cistern if all the taps are opened together?
1
Rate of first tap: \(\tfrac14\) per hour. Rate of second tap: \(\tfrac{1}{20}\) per hour. Rate of emptying tap: \(\tfrac{1}{20}\) per hour.
The second filling tap and the emptying tap exactly cancel out, leaving only the first tap's rate: \(\tfrac14\) per hour.
Time to fill one-fourth of the cistern: \(\dfrac{1/4}{1/4} = 1\) hour.
Hence, it takes 1 hour to fill one-fourth of the cistern.
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