Multiple choice

A cistern can be filled with water by a pipe in 9 hours and it can be emptied by a second pipe in 6 hours. If both the pipes are opened when the cistern is full, the time in which it will be emptied is:

  1. 18 hours

  2. 16 hours

  3. 14 hours

  4. 12 hours

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rate of filling = 1/9. Rate of emptying = 1/6. Net rate = 1/9 - 1/6 = (2-3)/18 = -1/18. The negative sign indicates emptying. It takes 18 hours to empty.

AI explanation

The filling pipe adds water at 1/9 per hour and the emptying pipe removes water at 1/6 per hour. The net rate of emptying is 1/6 minus 1/9. Finding a common denominator of 18 gives a net rate of 3/18 minus 2/18, which equals 1/18 per hour. The time to empty a full cistern is the reciprocal of the net rate, which is 18 hours.

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