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.