Mathematics · Time and Work

A bricklayer team consists of two masons A and B, and a mechanical brick feeder. Mason A alone can finish a wall in 12 days and Mason B alone can finish it in 15 days. When working, the mechanical brick feeder does the negative work of dismantling the wall at a rate equal to the positive work of a worker who finishes the wall in 10 days. Initially, the wall is 1/6th complete. Mason A works alone on the 1st day. On the 2nd day, Mason B joins and the brick feeder starts operating. The feeder works in a repetitive pattern: 3 consecutive days working, then 1 day broken/off. Find the total number of days taken from the start until the wall is completely finished.