Question

Первая труба может наполнить бассейн за 50 мин а две трубы вместе наполнят бассейн за 20 мин.Можно ли через одну вторую трубу наполнить бассейн за 33 мин ?

Answer 1

Первая труба за 1 час наполнит 1/20 часть бассейна

вторая труба за 1 час наполнит 1/15 часть бассейна

третья труба за 1 час наполнит 1/10 часть бассейна

вместе за 1 час: 1/20+1/15+1/10 = (3+4+6)/60 = 13/60 часть бассейна

за 2 часа: 2*13/60 = 26/60 часть бассейна

1/2 = 30/60 >26/60 половину бассейна не наполнят

1/3 = 20/60<26/60 - треть бассейна наполнят

Answer 2

Problem Analysis

We are given that the first pipe can fill a pool in 50 minutes, and two pipes together can fill the pool in 20 minutes. We need to determine if it is possible to fill the pool using both pipes in 33 minutes.

Solution

Let's assume that the first pipe can fill the pool at a rate of x units per minute, and the second pipe can fill the pool at a rate of y units per minute.

According to the given information, we have the following equations:

- First pipe: x * 50 = 1 (since it fills the pool in 50 minutes) - Both pipes together: (x + y) * 20 = 1 (since they fill the pool in 20 minutes)

We need to find out if it is possible to fill the pool using both pipes in 33 minutes. Let's calculate the rate at which both pipes fill the pool:

- Both pipes together: (x + y) * 33 = 1

To solve this problem, we can use a system of equations. We have three equations and three unknowns (x, y, and the volume of the pool). We can solve this system of equations to find the values of x and y.

Solution Steps

1. Solve the first equation to find the value of x. 2. Solve the second equation to find the value of y. 3. Substitute the values of x and y into the third equation to check if it is possible to fill the pool in 33 minutes.

Solution Details

1. Solve the first equation: - x * 50 = 1 - Divide both sides by 50: x = 1/50

2. Solve the second equation: - (x + y) * 20 = 1 - Substitute the value of x: (1/50 + y) * 20 = 1 - Simplify: (20/50 + 20y) = 1 - Multiply both sides by 50: 20 + 1000y = 50 - Subtract 20 from both sides: 1000y = 30 - Divide both sides by 1000: y = 3/100

3. Substitute the values of x and y into the third equation: - (x + y) * 33 = 1 - Substitute the values of x and y: ((1/50) + (3/100)) * 33 = 1 - Simplify: (2/100 + 3/100) * 33 = 1 - Simplify further: (5/100) * 33 = 1 - Multiply: 165/100 = 1 - Simplify: 1.65 = 1

Since 1.65 is not equal to 1, it is not possible to fill the pool using both pipes in 33 minutes.

Answer

No, it is not possible to fill the pool using both pipes in 33 minutes.