Pipe A is an inlet pipe that can fill an empty cistern in 69 hours. Pipe B can drain the filled cistern in 46 hours. When the cistern was filled the two pipes are opened one at a time for an hour each, starting with Pipe B. how long will it take for the cistern to be empty?

Pipe A can fill cistern in 69 hours.

Pipe B can empty cistern in 46 hours.

Let's assume total work = 138

Efficiency of A = 2

Efficiency of B = -3 (Subtraction sign is due to outlet pipe.)

For empty the cistern, Alternatively pipe B and A respectively work. So in every 2 hours 1 part of tank is empty out of total 138.

Then we can say that for emptying 135 parts, we need 270 hours and last 1 hour B will empty 3 parts.

So 270 + 1 = 271 hours

If we convert 271 hours in days by dividing 24. Then got 11 days 7 hours.