Multiple choice

Pipes P, Q and R can fill a tank in 24 hours. All the pipes are opened for 6 hours and then pipe P is closed. In another 30 hours, pipes Q and R fill the tank. How much time (in hours) does pipe P alone take to fill the tank?

  1. 30 hours

  2. 40 hours

  3. 60 hours

  4. 80 hours

  5. 65 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let rates be p, q, r. p+q+r = 1/24. In 6 hours, they do 6/24 = 1/4 work. Remaining work = 3/4. Q+R do 3/4 work in 30 hours, so q+r = (3/4)/30 = 1/40. Then p = (p+q+r) - (q+r) = 1/24 - 1/40 = (5-3)/120 = 2/120 = 1/60. P takes 60 hours.

AI explanation

Let the total capacity of the tank be the least common multiple of the times, which is 24 units. Pipes P, Q and R together fill 24 divided by 24, or 1 unit per hour. In the first 6 hours, they complete 6 units, leaving 18 units for pipes Q and R to fill. Pipes Q and R together fill 18 units in 30 hours, so their combined rate is 18 divided by 30, or 3 divided by 5 units per hour. The rate of pipe P is the total rate minus the rate of Q and R, which is 1 minus 3 divided by 5, or 2 divided by 5 units per hour. Therefore, pipe P alone requires 24 divided by 2 multiplied by 5, giving a total of 60 hours.

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