Question

Бассейн наполняется двумя трубами за 4 часа.Одна первая труба наполняет его на 6 часов быстрее,чем одна вторая.За какое время бассейн может наполнится каждой трубой в отдельности.

Answer 1

Х-время быстрой
х+6-время медленной
1-объем бассейна

1/х+1/(х+6)=1/4 умножим все на х(х+6)
х+6+х=0,25х(х+6)
2х+6=0,25х²+1,5х
0,25х²-0,5х-6=0 умножим на 4
х²-2х-24=0
D = (-2)² - 4·1·(-24) = 4 + 96 = 100
x1 = (2 - √100)/(2*1) = (2 - 10)/2 = -8/2 = -4 не подходит
x2= (2 +√100)/(2*1) = (2 + 10)/2 =12/2 =6ч-время быстрой трубы
6+6=12ч-время медленной трубы

Answer 2

Problem Analysis

We are given that a pool is being filled by two pipes in 4 hours. The first pipe fills the pool 6 hours faster than the second pipe. We need to find the time it takes for each pipe to fill the pool individually.

Solution

Let's assume that the second pipe takes x hours to fill the pool. Since the first pipe fills the pool 6 hours faster, it will take (x - 6) hours to fill the pool.

According to the problem, the combined time it takes for both pipes to fill the pool is 4 hours. We can set up the following equation based on the work done by each pipe:

1/(x - 6) + 1/x = 1/4

To solve this equation, we can find a common denominator and then simplify:

(x + x - 6)/(x(x - 6)) = 1/4 (2x - 6)/(x^2 - 6x) = 1/4

Cross-multiplying, we get:

4(2x - 6) = x^2 - 6x 8x - 24 = x^2 - 6x

Rearranging the equation, we have:

x^2 - 14x + 24 = 0

Now we can solve this quadratic equation to find the value of x.

Quadratic Equation Solution

Using the quadratic formula, we have:

x = (-b ± √(b^2 - 4ac))/(2a)

In this case, a = 1, b = -14, and c = 24. Substituting these values into the quadratic formula, we get:

x = (-(-14) ± √((-14)^2 - 4(1)(24)))/(2(1)) x = (14 ± √(196 - 96))/2 x = (14 ± √100)/2 x = (14 ± 10)/2

Simplifying further, we have:

x = (14 + 10)/2 or x = (14 - 10)/2 x = 24/2 or x = 4/2 x = 12 or x = 2

Since the time cannot be negative, we discard the solution x = 2. Therefore, the time it takes for the second pipe to fill the pool is 12 hours.

Since the first pipe fills the pool 6 hours faster, it will take (12 - 6) = 6 hours to fill the pool.

Answer

Therefore, the pool can be filled by the first pipe in 6 hours and by the second pipe in 12 hours.