Multiple choice

A reservoir has an inlet pipe (Pipe P) that can fill the reservoir in 18 hours and an outlet pipe (Pipe R) that can empty it in 30 hours. If the inlet pipe is opened alone for 6 hours and then the outlet pipe is also opened while the inlet pipe continues to run, how much additional time is required to fill the remaining part the reservoir completely?

  1. 15 hours

  2. 22 hours

  3. 24 hours

  4. 30 hours

  5. 34 hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Pipe P fills at 1/18 per hour, Pipe R empties at 1/30 per hour. In 6 hours, P fills 6/18 = 1/3 of the reservoir. Remaining 2/3 must be filled by (P-R), which is 1/18 - 1/30 = (5-3)/90 = 2/90 = 1/45 per hour. Time = (2/3) / (1/45) = 30 hours.

AI explanation

Let the total capacity be 90 units, making the rates of the inlet pipe P and outlet pipe R equal to 5 and -3 units per hour respectively. In the first 6 hours, pipe P alone fills 30 units, leaving 60 units to be filled. Once pipe R is opened, the net filling rate becomes 5 - 3 = 2 units per hour. Dividing the remaining 60 units by the net rate of 2 gives the additional time required, which is 30 hours.

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