Swimming pool

Cherry

New member
#1
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 \(a\)?

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