Question

Двумя насосами бассейн должны были заполнить за 8 часов, но за два часа до окончания работы один насос пришлось выключить, в результате чего заполнение бассейна заняло 9 часов. За сколько часов можно заполнить бассейн каждым из насосов по отдельности?

Answer 1

Вдвоем они за 6 часов закачали бассейн на 3/4. Оставшуюся четверть первый смог закачать за 3 часа. Значит первый насос сможет закачать воду в бассейн за 12 часов
1/12+1/x=1/8
1/x=3/24-2/24
1/x=1/24
x=24
второй насос сможет закачать воду в бассейн за 24 часа

Answer 2

Problem Analysis

We are given that two pumps can fill a pool in 8 hours. However, one of the pumps was turned off 2 hours before the completion of the work, resulting in the pool taking 9 hours to fill. We need to determine how long each pump would take to fill the pool individually.

Solution

Let's assume that the first pump can fill the pool in x hours and the second pump can fill the pool in y hours.

From the given information, we know that: - Both pumps together can fill the pool in 8 hours. - One pump was turned off 2 hours before the completion of the work, and the pool took 9 hours to fill.

Using this information, we can set up the following equation: 1/x + 1/y = 1/8 ---(1)

Since one pump was turned off 2 hours before the completion of the work, the remaining time for the second pump to fill the pool alone is 2 hours. Therefore, we can set up the following equation: 1/y = 1/2 ---(2)

Now, we can solve equations (1) and (2) simultaneously to find the values of x and y.

Calculation

Let's solve equations (1) and (2) to find the values of x and y.

From equation (2), we have: 1/y = 1/2 Multiplying both sides by 2y, we get: 2/y = 1 Cross-multiplying, we get: 2 = y

Substituting the value of y in equation (1), we have: 1/x + 1/2 = 1/8 Multiplying both sides by 8x, we get: 8 + 4x = x Simplifying the equation, we get: 4x = 8 Dividing both sides by 4, we get: x = 2

Therefore, the first pump can fill the pool in 2 hours, and the second pump can fill the pool in 4 hours.

Answer

Each pump can fill the pool individually in the following times: - The first pump can fill the pool in 2 hours. - The second pump can fill the pool in 4 hours.

Please let me know if I can help you with anything else.