Multiple choice

A tap can fill a cistern in 5 hours and another tap can empty the same cistern in 6 hours. How long will it take for the cistern to fill if both the taps are turned on?

  1. 25 hours

  2. 30 hours

  3. 37 hours

  4. 28 hours

  5. 19 hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The net rate of filling the cistern is (1/5 - 1/6) = 1/30 cisterns per hour. Therefore, it takes 30 hours to fill the cistern completely.

AI explanation

Using the net work equation, the first tap fills 1/5 of the cistern per hour while the second tap empties 1/6 of the cistern per hour. Working simultaneously, their combined net filling rate is 1/5 - 1/6 per hour. Finding a common denominator gives the net rate as (6 - 5)/30, which equals 1/30 of the cistern filled per hour. Therefore, it takes exactly 30 hours to fill the cistern.

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