A can do a piece of work in 15 days and B in 20 days. How much time will they take to complete the work if they work on alternate days, starting with A?

A's work rate is 1/15 per day, B's work rate is 1/20 per day. Working alternately starting with A, in 2 days they complete 1/15 + 1/20 = 4/60 + 3/60 = 7/60 of the work. After 16 days (8 cycles of 2 days), they complete 8 × 7/60 = 56/60, leaving 4/60. On day 17, A works and completes 1/15 = 4/60, finishing the job. Total time = 17 days.