Question

Первая труба пропускает на 9 литров воды в минуту меньше , чем вторая труба . сколько литров воды в минуту пропускает первая труба если резервуар объемом 216 литров она заполняет на 4 минуты дольше чем вторая труба

Answer 1

Пусть первая труба пропускает х литров в минуту, вторая тогда - х+9. Чтобы заполнить резервуар через первую трубу, тогда потребуется 216/х минут, а через вторую - 216/(х+9), и при этом верно:
216/х = 216/(х+9) + 4
Пробуем решить это уравнение:
216/х = 216/(х+9) + 4
216/х = (216+4(х+9))/(х+9)
216/х = (216+4х+36)/(х+9)
216/х = (252+4х)/(х+9)
216(х+9) = х(252+4х)
216х + 1944 = 252х + 4х^2
4x^2 + 36x - 1944 = 0
x^2 + 9x - 486 = 0
D = 9^2 + 4*486 = 81 + 1944 = 2025 = 45^2
x = (-9 +- 45)/2 = {-27; 18} - отрицательный корень явно не устраивает, отбрасываем. Значит искомый ответ - 18 литров в минуту.

Answer 2

Calculation of Water Flow Rate

To calculate the water flow rate of the first pipe, we can use the information provided. We know that the first pipe allows 9 liters less water per minute compared to the second pipe. Additionally, we know that the first pipe fills a reservoir with a volume of 216 liters in 4 minutes longer than the second pipe.

Let's assume that the water flow rate of the second pipe is x liters per minute.

According to the given information, the first pipe allows 9 liters less water per minute than the second pipe. Therefore, the water flow rate of the first pipe can be expressed as (x - 9) liters per minute.

We also know that the first pipe fills the reservoir in 4 minutes longer than the second pipe. This means that the time it takes for the first pipe to fill the reservoir is (t + 4) minutes, where t is the time taken by the second pipe to fill the reservoir.

Now, we can set up an equation to solve for the water flow rate of the first pipe.

The equation is as follows:

Water flow rate of the first pipe * Time taken by the first pipe = Water flow rate of the second pipe * Time taken by the second pipe

Substituting the given values into the equation, we have:

(x - 9) * (t + 4) = x * t

Simplifying the equation, we get:

xt - 9t + 4x - 36 = xt

Rearranging the equation, we have:

4x - 9t - 36 = 0

Now, we need additional information to solve for the water flow rate of the first pipe.