Question 13
There are four pipes installed in the pool. The first two pipes are used to fill the pool with water, while the remaining two pipes are responsible for draining water from the pool. If all four pipes are operational simultaneously, the reservoir fills up in $2.5$ hours. When only pipes $1$, $2$, and $3$ are in use, the pool fills up in $1.5$ hours. Similarly, when only pipes $1$, $3$, and $4$ are active, it takes $15$ hours to fill the pool. How long does it take for the pool to be full when only pipes $1$ and $3$ are operational?