A large tanker can be filled by pipe A in 60 minutes and by pipe B in 40 minutes. If pipe B runs alone for half the total filling time and both pipes A and B operate together during the remaining half, how long will it take to fill the tanker completely from empty?

Explanation

The combined filling rate of pipes A and B is (1/60 + 1/40) = 1/24 of the tank per minute. Let the total filling time be x minutes. Pipe B works alone for half the time, filling (x/2) * (1/40) of the tank, and both pipes work together for the other half, filling (x/2) * (1/24). The sum of these parts equals the whole tank: (x/2)*(1/40) + (x/2)*(1/24) = 1. Simplifying, x/2 * (1/40 + 1/24) = 1, which gives x/2 * (1/15) = 1, leading to x = 30 minutes.