A and B working separately can complete a piece of work in 10 and 16 days, respectively. If they work for a day alternately, with A beginning the work, in how many day(s) will the work be completed?

A

$$10\frac{1}{4}$$

B

$$12\frac{1}{4}$$

C

$$1\frac{1}{4}$$

D

$$\frac{1}{4}$$