Question

Первая труба наполняет резервуар на 6 минут дольше, чем вторая. Обе трубы наполняют этот же резервуар за 4 минуты. За сколько минут наполняет этот резервуар одна вторая труба?напишите решение за 8 класс,пожалуйста!:))))

Answer 1

1/х+3=4
1/х-1/у=6
где 1-объем всей работы а х-скорость первой трубы,у-скорость второй трубы
тогда выразим х из первого уравнения
х=1-4у/4
и подставим во второе
6ху=у-х
тогда
6у-24у^2/4=4у-1+4у/4
6у-24у^2-8у+1/4=0
умножаем обе части на 4 чтобы избавиться от знаментеля
24у^2+2у-1=0
D1=k^2-ac=1+24=25
y1=-1-5/24=-6/24 отбрасывпем данный корень т.к скорость величина всегда положительная
у2=-1+5/24=4/24=1/6
чтобы найти время нужно работу разделить на скорость то
1/1/6=6мин
ответ: 6мин

Answer 2

Solution for Filling the Tank

To solve this problem, we can use the concept of the rate of work. Let's denote the time taken by the first pipe as x minutes and the time taken by the second pipe as y minutes.

Given: - The first pipe fills the tank 6 minutes longer than the second pipe. - Both pipes together can fill the tank in 4 minutes.

We can set up the following equation based on the given information: 1. The rate of work of the first pipe is 1/x tanks per minute. 2. The rate of work of the second pipe is 1/y tanks per minute. 3. Together, the rate of work of both pipes is 1/4 tanks per minute.

Using the above information, we can form the equation: 1/x - 1/y = 1/6 .

Solving the Equation

To solve the equation 1/x - 1/y = 1/6, we can use the method of substitution or elimination. Let's solve it using the substitution method.

We can express 1/x in terms of 1/y as follows: 1/x = 1/y + 1/6.

Now, we know that both pipes together can fill the tank in 4 minutes. Therefore, their combined rate of work is 1/4 tanks per minute.

We can express the combined rate of work as: 1/x + 1/y = 1/4.

Solving the System of Equations

We have the following system of equations: 1. 1/x = 1/y + 1/6 2. 1/x + 1/y = 1/4

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

Conclusion

By solving the system of equations, we can determine the time taken by the second pipe to fill the tank.

Let's proceed with solving the system of equations to find the solution.