Multiple choice

Consider three pipes A, B and C connected to a tank. All three pipes can fill the tank in 6 hours. Pipe C is taken off after working at it for two hours and pipes A and B fill the remaining part of the tank in 7 hours. Determine the time required to fill the tank alone by pipe C.

  1. 6 hours

  2. 9 hours

  3. 14 hours

  4. 21 hours

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A+B+C = 1/6. In 2 hours, they fill 2/6 = 1/3. Remaining = 2/3. A+B fill 2/3 in 7 hours, so A+B = (2/3)/7 = 2/21. C = (A+B+C) - (A+B) = 1/6 - 2/21 = 7/42 - 4/42 = 3/42 = 1/14. C takes 14 hours.

AI explanation

Since all three pipes can fill the tank in 6 hours, their combined hourly rate is 1/6 of the tank. Working together for 2 hours, they fill 2/6 or 1/3 of the tank, leaving 2/3 of the tank empty. Pipes A and B complete this remaining 2/3 of the tank in 7 hours, meaning their combined hourly rate is (2/3) divided by 7, which equals 2/21 of the tank. Subtracting the rate of A and B from the total rate gives the rate of pipe C as (1/6 minus 2/21), which equals 1/14 per hour. Therefore, pipe C alone requires 14 hours to fill the tank.

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