A tank is connected to three pipes: A, B, and C. Pipe A can fill the tank in 4 hours, pipe B in 5 hours, while pipe C can drain it completely in 2 hours. If pipe A is opened at 1 AM, pipe B at 2 AM, and pipe C at 3 AM, at what time will the tank be empty?

Explanation

From 1 AM to 2 AM, only pipe A fills the tank, contributing 1/4 of the tank per hour. Between 2 AM and 3 AM, both pipes A and B work together, filling at a combined rate of 1/4 + 1/5 = 9/20 of the tank per hour. After 3 AM, all three pipes are open, with pipe C draining at 1/2 tank per hour. The net filling rate from 3 AM onward is 1/4 + 1/5 - 1/2 = -1/20 per hour, meaning the tank is being emptied. By calculating the total filled volume by 3 AM and dividing by the emptying rate, the tank will be completely empty 14 hours after 3 AM, which is at 5 PM.