Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6 hours.…

Step-by-Step Solution

First, determine the work rates of each pipe.

• Pipe A fills the tank in 8 hours, so its rate is 1/8 per hour.

• Pipe B fills the tank in 6 hours, so its rate is 1/6 per hour.

Next, calculate the work done when both pipes are open for 2 hours.

Combined rate = 1/8 + 1/6 = 3/24 + 4/24 = 7/24 per hour.

Work done in 2 hours = 2 × (7/24) = 14/24 = 7/12 of the tank.

Now, find the remaining work to be done by Pipe B alone.

Remaining work = 1 - 7/12 = 5/12 of the tank.

Finally, calculate the time Pipe B takes to fill the remaining 5/12.

Time = (Remaining Work) / (Rate of B) = (5/12) / (1/6) = (5/12) × 6 = 30/12 = 2.5 hours.

Therefore, Pipe B will fill the remaining tank in 2.5 hours.