An inlet pipe can fill an empty tank in $$4\frac{1}{2}$$ hours while an outlet pipe drains a completely filled tank in $$7\frac{1}{5}$$ hours. The tank is initially empty, and the two pipes are alternately opened for an hour each, till the tank is completely filled, starting with the inlet pipe. In how many hours will the tank be completely filled?

A

24

B

$$20\frac{1}{4}$$

C

$$20\frac{3}{4}$$

D

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