TWO pipes A and B can fill an empty tank in 10 hours and 16 hours respectively. They are opened alternately for 1 hour each, starting with pipe A first. In how many hours, the empty tank will be filled?

A

$$12\frac{1}{3}$$

B

$$12\frac{1}{8}$$

C

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

D

$$12\frac{1}{6}$$