Pipe A can fill an empty tank in 1.5 hours, while pipe B can empty a filled tank in 2.4 hours. When the tank is empty, pipe A is turned on and closed for one hour. Now pipe B is opened for one hour to drain the water from the tank and then closed. Pipes in the tank are alternately opened and closed for one hour each time. How long will it take to fill the tank completely?

Pipe A fills at 1/1.5 = 2/3 tank per hour. Pipe B empties at 1/2.4 = 5/12 tank per hour. In each 2-hour cycle (1 hr filling + 1 hr emptying), net fill = (2/3 - 5/12) = (8/12 - 5/12) = 3/12 = 1/4 tank. After 3 full cycles (6 hours), tank is 3/4 full. Hour 7 (filling): adds 2/3, making 3/4 + 2/3 = 9/12 + 8/12 = 17/12 = 1 5/12 - overflow means tank fills during this hour. Tank needs 1/4 more. Time needed = (1/4) / (2/3) = 3/8 hour = 0.375 hours. Total = 6 + 0.375 = 6.375 hours.