Question

Бассейн для плаванья наполняется водой двумя кранами за 1 час 12 мин. Если второй кран закрыть через 1 час, то для наполнения бассейна первый кран должен быть открыт еще в течение 20 мин. За какое время наполнится бассейн, если открыть только первый кран? Только второй кран (анализ решения задачи)?

Answer 1

Х бас/час - скорость наполнения бассейна через 1 кран
у бас/час - через 2 кран
(х+у) бас/час - скорость наполнения через 2 крана одновременно
1 - объем бассейна
1ч12мин=6/5час
20мин=1/3час
1/х+у) - время заполнения бассейна через 2 крана одновременно(=6/5час)
Два крана были открыты 1 час + второй был открыт 1/3час и бассейн был наполнен.
1/(х+у)=6/5 }
х+у+1/3у=1 }

6х+6у=5 }
х+1 ¹/₃у=1}
х=1 - 1 1/3у
6(1-1 1/3у)+6у=5
6-8у+6у=5
2у=1
у=1/2(бас/час) - скорость заполнения бассейна через ІІ кран
1:1/2=2(часа) - время заполнения бассейна через ІІ кран
1 - 1 1/3*1/2=1/3(бас/час) - скорость заполнения бассейна через І кран
1:1/3=3(часа) - время заполнения бассейна через І кран

Answer 2

Problem Analysis

We are given that a swimming pool is being filled with water using two taps. It takes 1 hour and 12 minutes to fill the pool with both taps open. If the second tap is closed after 1 hour, the first tap needs to remain open for an additional 20 minutes to fill the pool. We need to determine how long it would take to fill the pool if only the first tap is open.

Solution

Let's assume that the rate at which the first tap fills the pool is x units per minute, and the rate at which the second tap fills the pool is y units per minute.

From the given information, we can form the following equations:

1. When both taps are open, the pool is filled in 1 hour and 12 minutes: - (1 hour + 12 minutes) * (x + y) = 1 pool

2. If the second tap is closed after 1 hour, the first tap needs to remain open for an additional 20 minutes to fill the pool: - (1 hour + 20 minutes) * x = 1 pool

We can solve these equations to find the values of x and y and then determine the time it would take to fill the pool with only the first tap open.

Calculation

Let's convert the given time values into minutes for easier calculations:

- 1 hour = 60 minutes - 12 minutes = 12 minutes - 20 minutes = 20 minutes

Now, let's solve the equations:

1. From equation 1, we have: - (60 + 12) * (x + y) = 1 - 72 * (x + y) = 1

2. From equation 2, we have: - (60 + 20) * x = 1 - 80 * x = 1

Simplifying equation 2, we get: - x = 1/80

Substituting the value of x into equation 1, we get: - 72 * (1/80 + y) = 1

Simplifying equation 3, we get: - 1/80 + y = 1/72

Solving for y, we get: - y = 1/72 - 1/80

Now, we can calculate the time it would take to fill the pool with only the first tap open. Let's denote this time as t:

- t * x = 1 - t * (1/80) = 1 - t = 80

Therefore, it would take 80 minutes to fill the pool with only the first tap open.

Answer

If only the first tap is open, it would take 80 minutes to fill the pool.

Explanation

When both taps are open, it takes 1 hour and 12 minutes to fill the pool. If the second tap is closed after 1 hour, the first tap needs to remain open for an additional 20 minutes to fill the pool. This means that the first tap fills the pool at a faster rate than the second tap. By solving the given equations, we determined that the first tap fills the pool at a rate of 1/80 units per minute, and the second tap fills the pool at a rate of 1/72 - 1/80 units per minute. Therefore, if only the first tap is open, it would take 80 minutes to fill the pool.