Question

Первая труба пропускает на 4 литра воды в минуту меньше,чем вторая труба.Сколько литров в минуту пропускает первая труба,если резервуар объем 48 литров она заполняет на 2 минуты дольше,чем вторая труба.Сразу решение

Answer 1

Х - производительность 1-й трубы
х+4 - производительность 2-й трубы
48/х - время заполнения резервуара 1-й трубой
48/(х+4) - время заполнения резервуара 2-й трубой
уравнение: 48/х - 48/(х+4) = 2
48(х+4)-48х = 2х(х+4)
48*4 = 2х^2  + 8x
x^2 + 4x - 96 =0
D = 16 +4*96 = 400
x1 = (-4 - 20)/2 < 0 не подходит
x1 = (-4 + 20)/2 = 8
Ответ: 1-я труба пропускает в минуту 8 литров

Answer 2

Problem Analysis

We are given two pipes, and we need to determine the flow rate of the first pipe. We know that the first pipe allows 4 liters less water per minute compared to the second pipe. Additionally, we are given that the first pipe fills a reservoir with a volume of 48 liters in 2 minutes longer than the second pipe.

Solution

Let's assume the flow rate of the second pipe is x liters per minute. According to the problem, the flow rate of the first pipe is 4 liters less than the flow rate of the second pipe, so the flow rate of the first pipe can be represented as (x - 4) liters per minute.

We are also given that the first pipe fills a reservoir with a volume of 48 liters in 2 minutes longer than the second pipe. This means that the time taken by the first pipe to fill the reservoir is 2 minutes longer than the time taken by the second pipe. Let's represent the time taken by the second pipe as t minutes. Therefore, the time taken by the first pipe to fill the reservoir is (t + 2) minutes.

We can use the formula Flow Rate = Volume / Time to calculate the flow rates of the pipes.

For the second pipe: Flow Rate of the second pipe = Volume / Time Flow Rate of the second pipe = 48 liters / t minutes Flow Rate of the second pipe = 48 / t liters per minute

For the first pipe: Flow Rate of the first pipe = Volume / Time Flow Rate of the first pipe = 48 liters / (t + 2) minutes Flow Rate of the first pipe = 48 / (t + 2) liters per minute

According to the problem, the flow rate of the first pipe is 4 liters less than the flow rate of the second pipe. Therefore, we can set up the following equation:

Flow Rate of the first pipe = Flow Rate of the second pipe - 4 48 / (t + 2) = 48 / t - 4

To solve this equation, we can cross-multiply and simplify:

48t = 48(t + 2) - 4(t + 2) 48t = 48t + 96 - 4t - 8 48t - 48t = 96 - 8 - 4t 0 = 88 - 4t 4t = 88 t = 88 / 4 t = 22

Therefore, the time taken by the second pipe to fill the reservoir is 22 minutes. Now we can substitute this value back into the equation to find the flow rate of the first pipe:

Flow Rate of the first pipe = 48 / (t + 2) Flow Rate of the first pipe = 48 / (22 + 2) Flow Rate of the first pipe = 48 / 24 Flow Rate of the first pipe = 2 liters per minute

Answer

The first pipe has a flow rate of 2 liters per minute.