Question

В первом бассейне былл 1600 м в кубе воды,а во втором 1215 м в кубе. Чтобы вычистить первый бассейн, из него насосом выкачивают 65 м в кубе воды в час. Чтобы заполнить второй бассейн, в него насосом вливают 45 м в кубе воды в час. Через сколько часов объём воды в бассейнах будет равным, если оба насоса будут работать одновременно? (РЕШИТЕ УРАВНЕНИЕМ)

Answer 1

1600-65×x=1215+45×x
385=110x
x= 385/110
x=3.5 часа

Answer 2

Solution:

To solve this problem, we can use the concept of simultaneous equations to find the time it takes for the volumes of water in both pools to be equal.

Let's denote: - V1 as the volume of water in the first pool (initially 1600 m³) - V2 as the volume of water in the second pool (initially 1215 m³) - R1 as the rate at which water is pumped out of the first pool (65 m³/h) - R2 as the rate at which water is pumped into the second pool (45 m³/h) - t as the time in hours

We can use the formula: V1 - R1t = V2 + R2t to represent the change in volumes over time.

Calculation:

Using the formula, we can solve for t: 1600 - 65t = 1215 + 45t 1600 - 1215 = 45t + 65t 385 = 110t t = 385 / 110 t ≈ 3.5 hours

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