A and B working separately can do a piece of work in 21 and 24 days, respectively. If they work for a day alternately with A beginning the work, it would be completed in _________.

A

$$24\frac{1}{8}$$ days

B

$$21\frac{3}{8}$$ days

C

$$22\frac{3}{8}$$ days

D

$$22\frac{1}{8}$$ days