Question

Через два крана бак наполнился за 9 мин. Если бы был открыт только первый кран, то бак наполнился бы за 12 мин. За сколько минут наполнился бы бак через один второй кран?

Answer 1

Ответ:

$\frac{1}{9} \: - \: Производительность \: двух \: вместе \: за \: 1 \: минуту$

$\frac{1}{12} \: - \: Производительность \: первого \: за \: 1 \: минуту$

$\frac{1}{9} - \frac{1}{12} = \frac{4 - 3}{36} = \frac{1}{36} \: Производительность \: второго \: за \: 1 \: минуту$

Второе заполнит за 36 минут

Answer 2

Problem Analysis

We are given that a tank is filled in 9 minutes using two taps, and if only the first tap is open, the tank is filled in 12 minutes. We need to determine how long it would take to fill the tank using only the second tap.

Solution

Let's assume that the first tap fills the tank at a rate of x units per minute, and the second tap fills the tank at a rate of y units per minute.

From the given information, we know that when both taps are open, the tank is filled in 9 minutes. This can be expressed as:

1/x + 1/y = 1/9 We are also given that if only the first tap is open, the tank is filled in 12 minutes. This can be expressed as:

1/x = 1/12 To find the time it takes to fill the tank using only the second tap, we need to find the value of y.

Calculation

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

From equation we can solve for x:

1/x = 1/12

Cross-multiplying, we get:

12 = x

So, the rate of the first tap, x, is 12 units per minute.

Substituting the value of x into equation we can solve for y:

1/12 + 1/y = 1/9

Multiplying both sides of the equation by 12y, we get:

y + 12 = 12y/9

Simplifying the equation, we get:

y + 12 = 4y/3

Multiplying both sides of the equation by 3, we get:

3y + 36 = 4y

Subtracting 3y from both sides of the equation, we get:

36 = y

So, the rate of the second tap, y, is 36 units per minute.

Answer

Therefore, if only the second tap is open, the tank would be filled in 36 minutes.

References

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