Question

Первая труба пропускает на 1 литр воды в минуту меньше, чем вторая. сколько литров воды в минуту пропускает 2 труба, если резервуар объёмом 638 л она заполняет на 7 мин. быстрее, чем первая труба заполняет резервуар объёмом 812 л.

Answer 1

Х л/мин - 1я труба
(х+1) л/мин - 2я труба
$\frac{812}{x}$ мин - требуется 1й трубе
$\frac{638}{x+1}$ мин - требуется 2й трубе.
Вторя быстрее на 7 мин.
$\frac{812}{x}-\frac{638}{x+1}=7\\ 812x+812-638x=7x^2+7x,\ npu\ x \neq 0,x \neq -1\\ 7x^2-167x-812=0 \\ D=27889+22736=50625=225^2\\ x=\frac{167 \pm225}{14}$
По смыслу задачи выбираем положительный корень $x=\frac{167 +225}{14}=14$
14 л/мин - 1я труба => 14+1 = 15 л/мин - 2я труба.
Ответ: 15.

Answer 2

Calculation of Water Flow Rate

To calculate the water flow rate of the second pipe, we need to determine the flow rate of the first pipe and the time it takes to fill the reservoir for each pipe.

Let's denote the flow rate of the first pipe as Q1 (in liters per minute) and the flow rate of the second pipe as Q2 (in liters per minute).

According to the given information: - The first pipe fills the reservoir with a volume of 812 liters in a certain amount of time. - The second pipe fills the same reservoir with a volume of 638 liters in 7 minutes less time than the first pipe.

To find the flow rate of the first pipe, we can divide the volume of the reservoir (812 liters) by the time it takes to fill it. Similarly, for the second pipe, we can divide the volume of the reservoir (638 liters) by the time it takes to fill it.

Let's calculate the flow rate of the first pipe:

Q1 = Volume of Reservoir / Time taken by the first pipe

Q1 = 812 liters / (time taken by the first pipe)

Similarly, let's calculate the flow rate of the second pipe:

Q2 = Volume of Reservoir / Time taken by the second pipe

Q2 = 638 liters / (time taken by the second pipe)

Now, we need to find the time taken by the first pipe and the time taken by the second pipe.

According to the given information, the second pipe fills the reservoir 7 minutes faster than the first pipe. Therefore, the time taken by the second pipe is 7 minutes less than the time taken by the first pipe.

Let's denote the time taken by the first pipe as T1 (in minutes) and the time taken by the second pipe as T2 (in minutes).

We can express the relationship between T1 and T2 as:

T2 = T1 - 7 minutes

Now, we can substitute the values of T1 and T2 into the equations for Q1 and Q2 to calculate the flow rates.

Let's calculate the flow rate of the first pipe (Q1):

Q1 = 812 liters / T1

And the flow rate of the second pipe (Q2):

Q2 = 638 liters / T2

To find the flow rate of the second pipe, we need to substitute the value of T2 in terms of T1 into the equation for Q2:

Q2 = 638 liters / (T1 - 7 minutes)

Now, we can solve these equations to find the flow rates of the first and second pipes.

Please provide the time taken by the first pipe (T1) in minutes, and I will calculate the flow rate of the second pipe (Q2) for you.