Question

Бак летнего душа объемом 600 литров можно заполнить одним из двух насосов. Первый закачивает на 5 л/мин больше , чем второй, поэтому на заполнение всего бака он тратит на 6 минут меньше второго. Сколько л/мин закачивает второй насос?

Answer 1

Ответ 20
1)600:6=100
2)100:5=20
Ответ:второй насос закачивает 20 литров в минуту
-ВНИМАНИЕ ОТВЕТ ПИШЕТСЯ НЕ В СОКРАЩЕНИИ

Answer 2

Calculating the Pumping Rate of the Second Pump

To calculate the pumping rate of the second pump, we can use the information provided in the question and apply a simple mathematical approach.

Given: - Volume of the tank: 600 liters - Time taken by the first pump to fill the tank: 6 minutes less than the second pump - Pumping rate of the first pump: 5 liters per minute more than the second pump

Let's denote the pumping rate of the second pump as x liters per minute.

The time taken by the second pump to fill the tank can be represented as: \[ \frac{600}{x} \]

The time taken by the first pump to fill the tank is 6 minutes less than the time taken by the second pump, which can be represented as: \[ \frac{600}{(x+5)} \]

Equating the two time expressions, we can solve for the pumping rate of the second pump.

\[ \frac{600}{x} = \frac{600}{(x+5)} + 6 \]

Solving this equation will give us the pumping rate of the second pump.

Calculation

Using the given equation, we can solve for the pumping rate of the second pump:

\[ \frac{600}{x} = \frac{600}{(x+5)} + 6 \]

\[ 600(x+5) = 600x + 6x(x+5) \]

\[ 600x + 3000 = 600x + 6x^2 + 30x \]

\[ 0 = 6x^2 + 30x - 3000 \]

Solving the quadratic equation, we find: \[ x^2 + 5x - 500 = 0 \]

Using the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Where: - a = 1 - b = 5 - c = -500

\[ x = \frac{-5 \pm \sqrt{5^2 - 4*1*(-500)}}{2*1} \]

\[ x = \frac{-5 \pm \sqrt{25 + 2000}}{2} \]

\[ x = \frac{-5 \pm \sqrt{2025}}{2} \]

\[ x = \frac{-5 \pm 45}{2} \]

The two possible solutions are: \[ x_1 = \frac{-5 + 45}{2} = 20 \] \[ x_2 = \frac{-5 - 45}{2} = -25 \]

Since the pumping rate cannot be negative, the pumping rate of the second pump is 20 liters per minute.