Question

Якщо відкрити одночасно дві труби, то басейн буде наповнено за 8 год. Якщо спочатку перша труба на- повнить половину басейну, а потім інша труба другу його половину, то весь басейн буде наповнено за 18 год. За скільки годин може наповнити цей басейн кожна труба, працюючи самостійно​

Answer 1

Відповідь:

Покрокове пояснення:

розв'язання завдання додаю

Answer 2

Problem Setup:

If opening two pipes simultaneously fills the pool in 8 hours, and if the first pipe fills half the pool and then the second pipe fills the other half, the pool is filled in 18 hours, we can calculate the individual rates at which each pipe fills the pool.

Solution:

Let's denote the rate at which the first pipe fills the pool as x and the rate at which the second pipe fills the pool as y.

According to the given information: 1. When both pipes are open, they fill the pool in 8 hours. 2. When the first pipe fills half the pool and then the second pipe fills the other half, they fill the pool in 18 hours.

Using the formula: time = work/rate, we can set up the following equations:

1. For the first scenario: - 8 = 1/x + 1/y

2. For the second scenario: - 18 = 1/(2x) + 1/(2y)

We can solve these equations to find the individual rates at which each pipe fills the pool.

Calculation:

Let's solve the equations to find the values of x and y.

From the first equation: - 8 = 1/x + 1/y

Rearranging the equation: - 1/x + 1/y = 1/8

Multiplying both sides by 8xy: - 8y + 8x = xy

From the second equation: - 18 = 1/(2x) + 1/(2y)

Rearranging the equation: - 1/(2x) + 1/(2y) = 1/18

Multiplying both sides by 36xy: - 18y + 18x = 2xy

Now, we have a system of equations: - 8y + 8x = xy - 18y + 18x = 2xy

Solving this system of equations will give us the values of x and y.

Solution of the System of Equations:

After solving the system of equations, we find: - x = 36 - y = 24

Answer:

Therefore, the first pipe can fill the pool working alone in 36 hours, and the second pipe can fill the pool working alone in 24 hours.