Pipes A and B can fill a tank in 37.5 minutes and 45 minutes respectively. If both pipes are opened together but pipe B is closed after some time, after how many minutes should pipe B be turned off so that the tank fills in exactly 30 minutes?

Explanation

Let the time after which pipe B is closed be x minutes. The combined rate of filling by pipes A and B is (1/37.5 + 1/45) per minute. For the first x minutes, both pipes work, filling x(1/37.5 + 1/45) of the tank. For the remaining (30 - x) minutes, only pipe A fills the tank, contributing (30 - x)(1/37.5). The total filled amount equals 1 tank: x(1/37.5 + 1/45) + (30 - x)(1/37.5) = 1. Solving this equation yields x = 9 minutes.