In a reservoir system, there are four pipes: three inlet pipes (X, Y, and Z) and one outlet pipe W. Pipe X can fill the reservoir in 15 hours, pipe Y in 25 hours, and pipe Z in 35 hours. Pipe W can empty the full reservoir in 45 hours and it runs continuously. The inlet pipes operate one at a time in a repeating hourly rotation—X in the first hour, Y in the second, Z in the third, then back to X, and so on—starting with X. Assuming the reservoir is initially empty and all rates are constant, how long will it take to completely fill the reservoir?

Rates: X=1/15, Y=1/25, Z=1/35, W=-1/45. Cycle of 3 hours: (1/15 + 1/25 + 1/35) - 3/45 = (21+15+9)/315 - 1/15 = 45/315 - 21/315 = 24/315 = 8/105 per 3 hours. To fill 1, it takes roughly 105/8 * 3 = 39.375 hours. After 39 hours (13 cycles), filled = 13 * (8/105) = 104/105. Remaining = 1/105. Hour 40 (Pipe X): 1/105 + 1/15 = 8/105. Hour 41 (Pipe Y): 8/105 + 1/25 = 40/525 + 21/525 = 61/525. Hour 42 (Pipe Z): 61/525 + 1/35 = 61/525 + 15/525 = 76/525. Hour 43 (Pipe X): 76/525 + 1/15 = 76/525 + 35/525 = 111/525. This is getting complex; checking the option 42 hours 54 minutes.