Pipes A and B can fill a tank in 6 hours and 8 hours, respectively. Both pipes are opened together for 3 hours. After that pipe A is closed, and B continues to fill the tank. In how many hours will the tank be filled?

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Accepted Answer

Step 1: Calculate the rate of filling for each pipe.
- Pipe A fills the tank in 6 hours, so its rate is 1/6 tank per hour.
- Pipe B fills the tank in 8 hours, so its rate is 1/8 tank per hour.

Step 2: Calculate the combined rate when both pipes are open.
- Combined rate = 1/6 + 1/8 = (4/24) + (3/24) = 7/24 tank per hour.

Step 3: Calculate how much of the tank is filled in 3 hours with both pipes open.
- Amount filled = rate × time = (7/24) × 3 = 7/8 of the tank.

Step 4: Calculate the remaining part of the tank to be filled.
- Remaining = 1 - 7/8 = 1/8 of the tank.

Step 5: After 3 hours, pipe A is closed, so only pipe B fills the tank.
- Pipe B's rate = 1/8 tank per hour.

Step 6: Calculate the time taken by pipe B to fill the remaining 1/8 tank.
- Time = remaining / rate = (1/8) / (1/8) = 1 hour.

Step 7: Total time to fill the tank = 3 hours (both pipes) + 1 hour (pipe B alone) = 4 hours.

Therefore, the tank will be completely filled in 4 hours.

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