Question

первая и вторая труба наполняют бассейн за 18 часов.первая и третья за 12,а вторая и третья за 9.за сколько часов наполнят бассейн три трубы одновременно?

Answer 1

Пусть х у z -  скорости труб.

 

x + y = 1/18

x + z = 1/12

z + y = 1/9 

 

x = 1/18 - y

z = 1/9 - y

x + z = 1/12

 

1/18 - y + 1/9 - y = 1/12

2y = 1/6 - 1/12 = 1/12

y = 1/24

 

x + z + y = 1/12 + 1/24 = 3/24 = 1/8

 

Ответ: заполнят за 8 часов. 

Answer 2

Problem Setup

We are given the following information: - The first and second pipes can fill the pool in 18 hours. - The first and third pipes can fill the pool in 12 hours. - The second and third pipes can fill the pool in 9 hours.

Solution

To find out how long it will take for all three pipes to fill the pool together, we can use the concept of "work done" by each pipe in a unit of time.

Let's denote the rates of work for the first, second, and third pipes as A, B, and C respectively. The rates are inversely proportional to the time taken to fill the pool.

From the given information, we can set up the following equations:

1. The rate of work for the first and second pipes: - A + B = 1/18 (work done in 1 hour)

2. The rate of work for the first and third pipes: - A + C = 1/12 (work done in 1 hour)

3. The rate of work for the second and third pipes: - B + C = 1/9 (work done in 1 hour)

We can solve these equations to find the individual rates of work for each pipe and then calculate the time it will take for all three pipes to fill the pool together.

Calculation

Let's solve the system of equations to find the rates of work for each pipe:

1. A + B = 1/18 2. A + C = 1/12 3. B + C = 1/9

Adding equations (1), (2), and (3) together, we get: - 2A + 2B + 2C = 1/18 + 1/12 + 1/9 - 2A + 2B + 2C = 9/108 + 12/108 + 12/108 - 2A + 2B + 2C = 33/108 - A + B + C = 33/216 - A + B + C = 1/6

So, the combined rate of work for all three pipes is 1/6 (work done in 1 hour).

Therefore, it will take all three pipes 6 hours to fill the pool together.

Answer

So, the three pipes will fill the pool together in 6 hours.