A tank can be filled by pipe A in 4 hours and pipe B in 6 hours. At 8:00 a.m., pipe A was opened. At what time will the tank be filled if pipe B is opened at 9:00 a.m.?

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Accepted Answer

Step 1: Calculate the rate of filling for each pipe.
- Pipe A fills the tank in 4 hours, so its rate = 1/4 tank per hour.
- Pipe B fills the tank in 6 hours, so its rate = 1/6 tank per hour.

Step 2: Calculate how much of the tank is filled by pipe A alone from 8:00 a.m. to 9:00 a.m. (1 hour).
- Amount filled by A in 1 hour = 1/4 tank.

Step 3: Remaining tank to be filled after 9:00 a.m. = 1 - 1/4 = 3/4 tank.

Step 4: From 9:00 a.m. onwards, both pipes A and B are open.
- Combined rate = 1/4 + 1/6 = (3/12) + (2/12) = 5/12 tank per hour.

Step 5: Time required to fill remaining 3/4 tank at combined rate = (3/4) ÷ (5/12) = (3/4) × (12/5) = 36/20 = 9/5 = 1.8 hours.

Step 6: Convert 1.8 hours to hours and minutes.
- 0.8 hour = 0.8 × 60 = 48 minutes.
- So, 1.8 hours = 1 hour 48 minutes.

Step 7: Add this time to 9:00 a.m.
- 9:00 a.m. + 1 hour 48 minutes = 10:48 a.m.

Therefore, the tank will be filled at 10:48 a.m.

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