Pipes A, B and are attached to an empty cistern. While the first two can fill the cistern in 4 and 10 hours, respectively, the third can drain the cistern, when filled, in 6 hours. If all the three pipes are opened simultaneously whenthe cistern is half-full, how many hours will be needed to fill the cistern?

A

$$\frac{30}{11}$$

B

$$\frac{60}{11}$$

C

$$\frac{120}{11}$$

D

$$\frac{90}{11}$$