Multiple choice

Pipe A can fill a tank in 40 minutes. Pipe B can fill the same tank in 20 minutes. A leak at the bottom of the tank can empty the tank in 120 minutes. If both pipes are open and the tank is already half full, how long will it take to fill the tank?

  1. 7.5 minutes

  2. 5.5 minutes

  3. 6.5 minutes

  4. 7 minutes

  5. 9.5 minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rate of Pipe A = 1/40. Rate of Pipe B = 1/20. Rate of leak = -1/120. Combined rate = 1/40 + 1/20 - 1/120 = (3+6-1)/120 = 8/120 = 1/15. Tank is half full, so 1/2 tank remains. Time = (1/2) / (1/15) = 15/2 = 7.5 minutes.

AI explanation

Using the least common multiple method, let the total capacity of the tank be 120 liters. Pipe A fills at 3 liters per minute, pipe B fills at 6 liters per minute, and the leak empties at 1 liter per minute. When all are open, the net filling rate is 3 plus 6 minus 1, which equals 8 liters per minute. Since the tank is already half full, the remaining capacity to be filled is 60 liters. Dividing this remaining capacity by the net filling rate gives 60 divided by 8, which equals 7.5 minutes. The answer is 7.5 minutes.

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