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?

Answer 1

2 труба наполняет резервуар за x мин, а 1 труба за x+6 мин.
За 1 мин 2 труба наполнит 1/x часть, а 1 труба 1/(x+6) часть..
А вместе они за 1 мин наполнят 1/4 резервуара.
1/x + 1/(x+6) = 1/4
Умножим все уравнение на x, на x+6 и на 4
4(x+6) + 4x = x(x+6)
4x + 24 + 4x = x^2 + 6x
x^2 + 6x - 8x - 24 = 0
x^2 - 2x - 24 = 0
(x - 6)(x + 4) = 0
x1 = 6 мин
x2 = -4 мин < 0 - не подходит
Ответ: 6 мин.

Answer 2

Problem Analysis

We are given that the first pipe fills a reservoir 6 minutes longer than the second pipe, and both pipes together can fill the reservoir in 4 minutes. We need to determine how long it takes for the second pipe to fill the reservoir on its own.

Solution

Let's assume that the second pipe takes x minutes to fill the reservoir on its own. Since the first pipe takes 6 minutes longer, it would take (x + 6) minutes to fill the reservoir on its own.

When both pipes work together, they can fill the reservoir in 4 minutes. This means that in 1 minute, they can fill 1/4th of the reservoir.

To find the individual rates of the pipes, we can set up the following equation:

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

Simplifying this equation will give us the value of x, which represents the number of minutes it takes for the second pipe to fill the reservoir on its own.

Calculation

Let's solve the equation:

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

To eliminate the fractions, we can multiply both sides of the equation by 4x(x + 6):

4x + 4(x + 6) = x(x + 6)

Simplifying further:

4x + 4x + 24 = x^2 + 6x

Combining like terms:

8x + 24 = x^2 + 6x

Rearranging the equation:

x^2 - 2x - 24 = 0

Factoring the quadratic equation:

(x - 6)(x + 4) = 0

Setting each factor equal to zero:

x - 6 = 0 or x + 4 = 0

Solving for x:

x = 6 or x = -4

Since time cannot be negative, the second pipe takes 6 minutes to fill the reservoir on its own.

Answer

Therefore, the second pipe takes 6 minutes to fill the reservoir on its own.