Painter A can paint a building in 12 days while Painter B can paint it in 16 days. If A and B work on alternate days, and A starts the work on the first day, then the number of days required to paint the building is

A does $$\dfrac{1}{12}$$/day, B does $$\dfrac{1}{16}$$/day. Each pair of days (A then B): $$\dfrac{1}{12} + \dfrac{1}{16} = \dfrac{7}{48}$$.

After 6 pairs (12 days): $$\dfrac{42}{48} = \dfrac{7}{8}$$ done; $$\dfrac{1}{8}$$ remains.

Day 13 (A): does $$\dfrac{1}{12} = \dfrac{4}{48}$$, leaving $$\dfrac{1}{24} = \dfrac{2}{48}$$.

Day 14 (B): needs $$\dfrac{1/24}{1/16} = \dfrac{2}{3}$$ of a day.

Total $$= 13\dfrac{2}{3}$$ days.