## 9. Pools and Pipes

The hotel has three pools $A, B$, and $C$ that can be connected or separated by valves. Several identical pipes are used for filling. When all three pools are connected, filling them with water from three pipes takes 18 minutes. If only pools $A$ and $B$ are connected, filling them with two pipes takes 21 minutes, and if only pools $B$ and $C$ are connected, filling them with two pipes takes 14 minutes. How many seconds does it take to fill pool $B$ with one pipe?

Result: $\quad 960$
## Solution.

One pipe would fill pools A, B, and C in $3 \cdot 18=54$ minutes, pools A and B in $2 \cdot 21=42$ minutes, and pools B and C in $2 \cdot 14=28$ minutes.

Therefore, one pipe would fill pool C in $54-42=12$ minutes, and pool A in $54-28=26$ minutes, from which it follows that it would fill pool B in $54-12-26=16$ minutes.

16 minutes $=16 \cdot 60$ seconds $=960$ seconds