# Swimming pool

#### Cherry

##### New member
Tanner wants to fill his swimming pool using two hoses, each of which sprays water at a constant rate. Hose A fills the pool in $$a$$ hours when used by itself, where $$a$$ is a positive integer. Hose B fills the pool in $$b$$ hours when used by itself, where $$b$$ is a positive integer. When used together, Hose A and Hose B fill the pool in 6 hours. How many different possible values are there for $$a$$?

$$\textbf{(A)}\ 5\qquad \textbf{(B)}\ 6\qquad \textbf{(C)}\ 9\qquad \textbf{(D)}\ 10\qquad \textbf{(E)}\ 12\qquad$$