Question

Бак имеет два крана. Если мы открываем только первый, депозит заполняется за 8 часов; и если мы откроем оба крана, он наполнится за 3 часа. Сколько времени потребуется, чтобы наполниться, если мы откроем только второй кран? Нужен развёрнутый ответ.

Answer 1

Пошаговое объяснение:

Если открыть 1 кран то депозит заполнится за 8 часов:

А если откроем оба крана то наполнится за 3 часа:

Решение:

Надо найти час заполнение второго крана

$\frac{1}{8} + \frac{1}{x} = \frac{1}{3} \\ x = \frac{1}{3} - \frac{1}{8} \\ x = \frac{5}{24} = \\ 24 \div 5 = 4.8$

Наполняется за 24 часа

Answer 2

Problem Analysis

We have a tank with two taps. If we open only the first tap, the tank fills up in 8 hours. If we open both taps, the tank fills up in 3 hours. We need to determine how long it will take to fill the tank if we only open the second tap.

Solution

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

According to the given information: - If we open only the first tap, the tank fills up in 8 hours. - If we open both taps, the tank fills up in 3 hours.

Using this information, we can set up the following equations:

Equation 1: x * 8 = 1 (since the tank fills up in 8 hours with only the first tap open)

Equation 2: (x + y) * 3 = 1 (since the tank fills up in 3 hours with both taps open)

We can solve these equations to find the values of x and y.

Solving the Equations

Let's solve Equation 1 for x:

x * 8 = 1

Dividing both sides by 8:

x = 1/8

Now, let's solve Equation 2 for y:

(x + y) * 3 = 1

Substituting the value of x:

(1/8 + y) * 3 = 1

Multiplying both sides by 8:

3/8 + 3y = 8/8

Simplifying:

3y = 5/8

Dividing both sides by 3:

y = 5/24

Answer

Therefore, the first tap can fill the tank at a rate of 1/8 units per hour, and the second tap can fill the tank at a rate of 5/24 units per hour.

To find out how long it will take to fill the tank if we only open the second tap, we can set up the following equation:

y * t = 1 (where t is the time in hours)

Substituting the value of y:

(5/24) * t = 1

Simplifying:

t = 24/5

So, it will take 24/5 hours to fill the tank if we only open the second tap.

Conclusion

If we open only the second tap, it will take 24/5 hours to fill the tank.

Note: The sources provided do not contain relevant information for this specific problem.