Three pipes, P, Q and R, together take four hours to fill a tank. All the three pipes were opened at the same time. After three hours, P was closed, and Q and R filled the remaining tank in two hours. How many hours will P alone take to fill the tank?

Question

Accepted Answer

Step 1: Let the rates of pipes P, Q, and R be p, q, and r respectively (in tank/hour).

Step 2: Given that all three pipes together fill the tank in 4 hours, so their combined rate is:
(p + q + r) = 1/4 tank per hour.

Step 3: They work together for 3 hours, so amount filled in 3 hours = 3 * (p + q + r) = 3/4 of the tank.

Step 4: Remaining tank to fill = 1 - 3/4 = 1/4.

Step 5: After 3 hours, P is closed. Q and R fill the remaining 1/4 tank in 2 hours.
So, rate of Q and R together = (1/4) / 2 = 1/8 tank per hour.

Step 6: From step 2, p + q + r = 1/4
From step 5, q + r = 1/8

Step 7: Subtracting, p = (p + q + r) - (q + r) = 1/4 - 1/8 = 1/8 tank per hour.

Step 8: Time taken by P alone to fill the tank = 1 / p = 1 / (1/8) = 8 hours.

Therefore, pipe P alone will take 8 hours to fill the tank.

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