Soru

Three water pipes, $A$, $B$, and $C$, are used to fill a storage tank. The filling rates of pipes $A$ and $B$ are in the ratio $3 : 2$, while the filling rates of pipes $B$ and $C$ are in the ratio $4 : 3$. Pipes $A$ and $B$ are opened together for $5\text{ hours}$, after which pipe $A$ is closed. Pipes $B$ and $C$ are then opened together for $10\text{ hours}$ to completely fill the remaining capacity of the tank. How many hours would pipe $A$ alone take to fill the entire empty tank?