Question

Через велику трубу басейн наповнюється водою за 9 год, а а через малу — за 12 год. Яку частину басейну залишається наповнити після 4 год спільної роботи обох труб?

Answer 1

1-(4/9+4/12)=36/36-(16/36+12/36)=36/36-28/36=8/36=2/9

Answer 2

Problem Analysis

We are given two pipes, a large pipe and a small pipe, that fill a pool with water. The large pipe fills the pool in 9 hours, while the small pipe fills the pool in 12 hours. We need to determine the fraction of the pool that remains to be filled after 4 hours of both pipes working together.

Calculation

To solve this problem, we can calculate the rates at which each pipe fills the pool and then determine the combined rate when both pipes are working together. We can then use this combined rate to find the fraction of the pool that remains to be filled after 4 hours.

Let's assume that the capacity of the pool is 1 unit (this assumption does not affect the final result).

The rate at which the large pipe fills the pool is 1/9 units per hour, and the rate at which the small pipe fills the pool is 1/12 units per hour.

When both pipes are working together, their combined rate is the sum of their individual rates. Therefore, the combined rate is (1/9 + 1/12) units per hour.

After 4 hours of both pipes working together, the amount of water filled is equal to the combined rate multiplied by the time. Therefore, the amount of water filled after 4 hours is (4 * (1/9 + 1/12)) units.

To find the fraction of the pool that remains to be filled, we subtract the amount of water filled from the total capacity of the pool. Therefore, the fraction of the pool that remains to be filled after 4 hours is (1 - 4 * (1/9 + 1/12)).

Calculation Result

After performing the calculations, we find that the fraction of the pool that remains to be filled after 4 hours of both pipes working together is 11/36.

Conclusion

After 4 hours of both the large and small pipes working together, approximately 11/36 of the pool remains to be filled.