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

Explanation

Pipe A fills the tanker in 60 minutes, so its rate is 1/60 per minute. Pipe B fills it in 40 minutes, so its rate is 1/40 per minute. Let the total time be T minutes. For the first half (T/2), only pipe B works, filling (1/40)*(T/2) of the tanker. For the second half (T/2), both pipes work together, filling (1/60 + 1/40)*(T/2) of the tanker. The sum of these fractions equals 1 (the full tanker): (T/2)*(1/40) + (T/2)*(1/60 + 1/40) = 1. Simplifying, T/2*(1/40 + 1/60 + 1/40) = 1, which leads to T = 30 minutes.