Question

Большой насос перекачивает за час на 2 м3 воды больше, чем средний, а средний — на 2 м3 больше, чем малый насос. Два средних и два малых насоса, работая вместе, наполнили резервуар емкостью 48 м3. Сразу после этого были включены два средних и два больших насоса, которые наполнили другой резервуар той же емкости. На всю работу затрачено 9 ч. Сколько кубометров воды перекачивает в час средний насос?ПОЛНОЕ ОПИСАНИЕ РЕШЕНИЯ, ПОЖАЛУЙСТА!

Answer 1

Х-производительность малого насоса
х+2-производительность среднего насоса
х+2+2=х+4 - производительность большого насоса
48/(2х+2(х+2))+48/(2(х+2)+2(х+4))=9
48(1/(2х+2х+4)+1/(2х+4+2х+8))=9
48(1/(4х+4)+1/(4х+12))=9
1/(4х+4)+1/(4х+12)=9/48 домножим на (4х+4)(4х+12)
4х+12+4х+4=0,1875(4х+4)(4х+12)
8х+16=0,1875(16х²+48х+16х+48)
8х+16=0,1875(16х²+64х+48)
8х+16=3х²+12х+9
3х²+4х-7=0
Д=100
х₁=-2 1/3-не подходит
х₂=1-производительность малого насоса
1+2=3 м³ в час-производительность среднего насоса

Answer 2

Problem Analysis

We are given information about three types of pumps: large, medium, and small. The large pump can pump 2 cubic meters (m³) more water per hour than the medium pump, and the medium pump can pump 2 m³ more water per hour than the small pump. We need to determine the hourly pumping capacity of the medium pump.

We are also given that two medium pumps and two small pumps, working together, filled a reservoir with a capacity of 48 m³. After that, two medium pumps and two large pumps were turned on and filled another reservoir of the same capacity. The total time taken for all the pumping was 9 hours.

Solution

Let's assume the hourly pumping capacity of the small pump is x m³.

According to the given information: - The large pump can pump 2 m³ more water per hour than the medium pump. - The medium pump can pump 2 m³ more water per hour than the small pump.

Therefore, the hourly pumping capacity of the medium pump is x + 2 m³, and the hourly pumping capacity of the large pump is x + 4 m³.

We are also given that two medium pumps and two small pumps, working together, filled a reservoir with a capacity of 48 m³. This can be represented by the equation:

2(x + 2) + 2x = 48

Simplifying the equation: 4x + 4 = 48 4x = 44 x = 11

So, the hourly pumping capacity of the small pump is 11 m³, the medium pump is 11 + 2 = 13 m³, and the large pump is 11 + 4 = 15 m³.

Now, we need to find out how much water the medium pump can pump in one hour. Since we know that the medium pump can pump 2 m³ more water per hour than the small pump, the hourly pumping capacity of the medium pump is 13 m³.

Therefore, the medium pump can pump 13 cubic meters of water per hour.

Answer

The medium pump can pump 13 cubic meters of water per hour.

Explanation

To solve this problem, we first assume the hourly pumping capacity of the small pump as x m³. Then, using the given information, we set up an equation and solve for x. After finding the value of x, we can determine the hourly pumping capacity of the medium pump, which is x + 2 m³. In this case, the value of x is 11, so the hourly pumping capacity of the medium pump is 13 m³.