Question

785. В первом бассейне было 1600 м3 воды, а во втором - 1215 м. Чтобы вычистить первый бассейн, из него насосом выкачивают 65 м3 воды в час. Чтобы наполнить второй бассейн, в него насосом заливают 45 м3 воды в час. Через сколько часов объемы воды в бассейнах ста- нут равными, если оба насоса будут работать одновременно? 12​

Answer 1

Ответ:

3,5 часа

Пошаговое объяснение:

Объем воды в первом бассейне в зависимости от прошедшего времени описывается уравнением:

v1 = 1600 - 65 * t

Объем воды во втором бассейне в зависимости от прошедшего времени описывается уравнением:

v2 = 1215 + 45 * t

объем воды будет равным:

1600 - 65 * t = 1215 + 45 * t

1600 - 1215 = 45t + 65t

385 = 110t

t = 385 / 110 = 3,5 часа

Answer 2

To find out how long it will take for the volumes of water in the two pools to become equal when both pumps are working simultaneously, we need to determine the rate at which the water levels change in each pool.

In the first pool, the pump removes 65 m³ of water per hour, while in the second pool, the pump adds 45 m³ of water per hour.

Let's calculate the time it takes for the volumes of water in the two pools to become equal:

Calculation:

Let's assume it takes t hours for the volumes of water in the two pools to become equal.

In the first pool, the volume of water decreases by 65 m³ per hour, so the equation for the first pool can be written as: 1600 - 65t = V₁

In the second pool, the volume of water increases by 45 m³ per hour, so the equation for the second pool can be written as: 1215 + 45t = V₂

To find the time it takes for the volumes of water in the two pools to become equal, we need to solve the equation: 1600 - 65t = 1215 + 45t

Solution:

Let's solve the equation:

1600 - 65t = 1215 + 45t

First, let's simplify the equation by combining like terms:

385 = 110t

Next, let's isolate the variable t by dividing both sides of the equation by 110:

t = 385 / 110

Now, let's calculate the value of t:

t ≈ 3.5

Therefore, it will take approximately 3.5 hours for the volumes of water in the two pools to become equal when both pumps are working simultaneously.

Please note that this is an approximate value and may vary depending on the actual rates of water flow and other factors.