Question

два одинаковых бассейна одновременно начали заполняться водой.В первый бассейн поступает в час на 30 м. куб больше воды, чем во второй . В некоторый момент в двух бассейнах оказалось столько воды, сколько составляет объем каждого из них. После этого через 2 ч 40 минут наполнился первый бассейн, а еще через 3 ч 20 мин - второй. Сколько воды поступало в час в каждый бассейн?

Answer 1

2ч 40мин+3ч 20мин=6час

2ч 40мин=2 2/3час

Чтобы наполнилось воды объемом один бассейн,вода должна поступать

в I бассейн 2 2/3 час, а во  II бассейн - 6 часов.

 

х м3/ч - воды поступает во II бассейн

(х+30) м3/ч - воды поступает в I бассейн

 

6х=2 2/3(х+30)

6х-2 2/3х=80

3 1/3х=80

х=24(м3/ч) - поступало воды во II бассейн

24+30=54(м3/ч) - воды поступало в I  бассейн

Answer 2

Problem Analysis

We have two identical swimming pools that are being filled with water simultaneously. The rate at which water is entering the first pool is 30 cubic meters per hour more than the rate at which water is entering the second pool. At a certain moment, both pools have the same amount of water, which is equal to the volume of each pool. After that, the first pool takes 2 hours and 40 minutes to fill completely, while the second pool takes 3 hours and 20 minutes to fill completely. We need to find the rate at which water is entering each pool per hour.

Solution

Let's assume that the rate at which water is entering the second pool is x cubic meters per hour. Therefore, the rate at which water is entering the first pool is (x + 30) cubic meters per hour.

We know that the volume of each pool is equal to the amount of water in both pools at the moment when they have the same amount of water. Let's denote this volume as V.

The time it takes to fill a pool is equal to the volume of the pool divided by the rate at which water is entering the pool. Therefore, we can write the following equations:

For the first pool: V = (x + 30) * (2 + 40/60) = (x + 30) * (2.67) For the second pool: V = x * (3 + 20/60) = x * (3.33) We can solve these equations to find the value of x, which represents the rate at which water is entering the second pool per hour.

Calculation

Let's solve the equations and to find the value of x.

(x + 30) * (2.67) = x * (3.33)

Simplifying the equation:

2.67x + 80.1 = 3.33x

0.66x = 80.1

x = 80.1 / 0.66

x ≈ 121.36

Therefore, the rate at which water is entering the second pool is approximately 121.36 cubic meters per hour.

To find the rate at which water is entering the first pool, we can substitute the value of x into the equation (x + 30):

Rate for the first pool = 121.36 + 30 = 151.36 cubic meters per hour.

Answer

The rate at which water is entering each pool per hour is approximately: - First pool: 151.36 cubic meters - Second pool: 121.36 cubic meters

Please note that these values are approximate due to rounding.

Let me know if you need any further assistance!