Question

Через первую трубу бассейн можно наполнить за 10 часов,а через другую - за 8 часов. Какую часть бассейна осталось наполнить,если обе трубы были открыты на протяжении 2 часов? Спасибо тем кто решит!(и баллы!)

Answer 1

Работу (т.е. наполнение бассейна) берем за единицу, тогда производителоьности труб будут 1/10 и 1/8 соответственно
составим уравнение:
т.к трубы были открыты вместе, то общая производительность, с  которой наполнялся бассейн будет равна: (0,1+0,125) (перехожу в десятичные дроби для удобства счета)
время, которое две трубы были открыты вместе=2 часам
следовательно:
(0,1+0,125)*2+оставшаяся часть бассейна =1 (целиковому бассейну)
решая данное уравнение, получаем: 0,45+ост. часть=1, значит отсавшаяся часть равна 0,55
Ответ: 0,55

Answer 2

Problem Analysis

We are given two pipes, one of which can fill a pool in 10 hours and the other in 8 hours. Both pipes were open for 2 hours. We need to determine the fraction of the pool that remains to be filled.

Solution

To solve this problem, we can calculate the rate at which each pipe fills the pool and then determine the fraction of the pool that remains to be filled after 2 hours.

Let's assume the capacity of the pool is 1 unit.

The first pipe can fill the pool in 10 hours, so its filling rate is 1/10 units per hour.

The second pipe can fill the pool in 8 hours, so its filling rate is 1/8 units per hour.

Since both pipes were open for 2 hours, the amount of water filled by the first pipe is (1/10) * 2 = 1/5 units.

Similarly, the amount of water filled by the second pipe is (1/8) * 2 = 1/4 units.

The total amount of water filled by both pipes is (1/5) + (1/4) = 9/20 units.

Therefore, the fraction of the pool that remains to be filled is 1 - (9/20) = 11/20.

Answer: The fraction of the pool that remains to be filled after both pipes were open for 2 hours is 11/20.

Explanation

After 2 hours, the first pipe fills 1/5 units of the pool, and the second pipe fills 1/4 units of the pool. The total amount of water filled by both pipes is 9/20 units. Therefore, the fraction of the pool that remains to be filled is 11/20.

Example Calculation

Let's calculate the fraction of the pool that remains to be filled using the given information:

The first pipe fills the pool in 10 hours, so its filling rate is 1/10 units per hour.

The second pipe fills the pool in 8 hours, so its filling rate is 1/8 units per hour.

Both pipes were open for 2 hours.

The amount of water filled by the first pipe is (1/10) * 2 = 1/5 units.

The amount of water filled by the second pipe is (1/8) * 2 = 1/4 units.

The total amount of water filled by both pipes is (1/5) + (1/4) = 9/20 units.

Therefore, the fraction of the pool that remains to be filled is 1 - (9/20) = 11/20.

Answer: The fraction of the pool that remains to be filled after both pipes were open for 2 hours is 11/20.