Question

Первая труба пропускает на 9 литров воды в минуту меньше, чем вторая труба. Сколько литров воды в минуту пропускает вторая труба, если резервуар объёмом 216 литров она заполняет на 4 минуты быстрее, чем первая труба?

Answer 1

Ответ:

Пошаговое объяснение:

первая Х л/мин

вторая х+9

216/х-216/(х+9)=4

Х^2+9Х-486=0 х=18

18+9=27 л/мин

Answer 2

Problem Analysis

We are given that the first pipe allows 9 liters of water per minute less than the second pipe. We also know that the second pipe fills a reservoir with a volume of 216 liters in 4 minutes faster than the first pipe. We need to determine how many liters of water per minute the second pipe allows.

Solution

Let's assume that the first pipe allows x liters of water per minute. According to the given information, the second pipe allows 9 liters per minute more than the first pipe, so the second pipe allows (x + 9) liters of water per minute.

We are also told that the second pipe fills a reservoir with a volume of 216 liters in 4 minutes faster than the first pipe. This means that the second pipe fills the reservoir in 4 minutes less time than the first pipe.

To solve this problem, we can set up the following equation based on the information given:

216 / x = 216 / (x + 9) + 4

Let's solve this equation to find the value of x, which represents the number of liters of water per minute allowed by the first pipe.

Calculation

To solve the equation, we can start by multiplying both sides by x(x + 9) to eliminate the denominators:

216(x + 9) = 216x + 4x(x + 9)

Expanding and simplifying the equation:

216x + 1944 = 216x + 4x^2 + 36x

Rearranging the terms:

4x^2 + 36x - 1944 = 0

Dividing the equation by 4 to simplify:

x^2 + 9x - 486 = 0

Now we can solve this quadratic equation. We can either factor it or use the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 9, and c = -486. Substituting these values into the quadratic formula:

x = (-9 ± √(9^2 - 4(1)(-486))) / (2(1))

Simplifying further:

x = (-9 ± √(81 + 1944)) / 2

x = (-9 ± √2025) / 2

x = (-9 ± 45) / 2

We have two possible solutions:

x1 = (-9 + 45) / 2 = 36 / 2 = 18 x2 = (-9 - 45) / 2 = -54 / 2 = -27

Since the number of liters of water per minute cannot be negative, we discard the negative solution. Therefore, the first pipe allows 18 liters of water per minute.

To find the number of liters of water per minute allowed by the second pipe, we add 9 to the value of x:

x + 9 = 18 + 9 = 27

Therefore, the second pipe allows 27 liters of water per minute.

Answer

The second pipe allows 27 liters of water per minute.