# Through the first pipe, the pool can be filled in 12 hours, and through the second – in 24 hours.

Through the first pipe, the pool can be filled in 12 hours, and through the second – in 24 hours. After several hours of filling the pool through both pipes, the first pipe was closed. The rest of the pool volume was filled for 9 hours through the second pipe. How many hours was the second chimney open?

1. The first pipe fills the pool in time: T1 = 12 hours;

2. The second pipe fills it in: T2 = 24 hours;

3. The rate of filling the first pipe: V1 = 1 / T1 (1 / hour);

4. Speed ​​of filling the second pipe: V2 = 1 / T2 (1 / hour);

5. The total speed of filling the pool: Vo (1 / hour);

Vo = V1 + V2 = 1/12 + 1/24 = 3/24 = 1/8 (1 / hour);

6. Time of filling the pool with two pipes: T4 hours;

7. Time of filling the rest of the pool with the second pipe: T3 = 9 hours;

8. During this time, the following will be filled: P2 part;

P2 = V2 * T3 = (1/24) * 9 = 3/8 part;

9. Together the pipes filled: Po part;

Po = 1 – P2 = 1 – 3/8 = 5/8 part;

10. This part will be filled in time: To hour;

To = Po / Vo = (5/8) / (1/8) = 5 hours;

11. Total time of filling the pool: T hour;

T = To + T3 = 5 + 9 = 14 hours.

Answer: the second pipe was open 14 hours.

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