Multiple choice

A tank is fitted with two inlet pipes, P and Q, and one outlet pipe, R. Pipe P can fill the tank in 4 hours, Q can fill it in 6 hours, and R can empty it in 8 hours. If P and Q are opened for 1 hour, and then R is also opened, how much total time will it take to fill the tank?

  1. 2 hours

  2. 3 hours

  3. 4 hours

  4. 5 hours

  5. 6 hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

P fills 1/4, Q fills 1/6, R empties 1/8 per hour. In 1 hour, P+Q fill 1/4 + 1/6 = 5/12. Remaining = 7/12. With R open, net rate = 1/4 + 1/6 - 1/8 = (6+4-3)/24 = 7/24. Time to fill remaining = (7/12) / (7/24) = 2 hours. Total time = 1 + 2 = 3 hours.

AI explanation

Assume the total tank capacity is 24 units, so pipes P, Q, and R have rates of 6, 4, and -3 units per hour respectively. In the first hour, P and Q fill 10 units of the tank. When R is opened, the net filling rate becomes 6 + 4 - 3 = 7 units per hour. The remaining 14 units take 14/7 = 2 hours to fill, making the total time 1 + 2 = 3 hours.

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