Question

Игорь и Паша красят забор за 10 часов.Паша и Володя красят этот же забор за 12 часов,а Володя и Игорь - за 15 часов.За сколько минут мальчики покрасят забор,работая втроем?

Answer 1

1 - вся работа
х (1/ч) - производительность Игоря
у (1/ч) - производительность Паши
z (1/ч) - производительность Володи
{1  + 1  =  1  
 х     у      10
{1  +  1  =  1  
 у      z      12
{1  +   1  =  1  
 z       x      15 
1  = 1  -  1 
x     10    y
1 =  1 - 1 
z    12   y
1  = 1  -  1  =  1  -  1  +  1  = 10 - 15 + 1  =  - 1  + 1
z     15    x     15    10    y         150     y       30    y
-1 + 1 = 1 - 1
30   y    12  y
1 + 1 =  1 + 1 
y    y    12   30
2 =  5 + 2
y        60
2  =  7 
y     60
1 = 7  
y   120
1 =  1 -  7    =12-7  =  5   
х    10  120     120     120
1 = 1  - 7    =  10-7  =  3  
z    12  120      120     120
1 + 1 + 1 = 7  +  5  +  3   =   15  =  1  - общая производительность всех
x    y    z         120              120     8      троих ребят
8 ч = 8*60=480 (мин) - втроем ребята покрасят забор.
Ответ: 480 мин

Answer 2

Problem Analysis

We are given the information that Igor and Pasha can paint a fence in 10 hours, Pasha and Volodya can paint the same fence in 12 hours, and Volodya and Igor can paint the fence in 15 hours. We need to determine how many minutes it will take for the three boys to paint the fence together.

Solution

To solve this problem, we can use the concept of work rates. The work rate is defined as the amount of work done per unit of time. If we assume that the work required to paint the fence is 1 unit, we can calculate the work rates of each pair of boys.

Let's denote the work rate of Igor and Pasha as R1, the work rate of Pasha and Volodya as R2, and the work rate of Volodya and Igor as R3.

We can calculate the work rates using the formula:

Work Rate = Work / Time

For Igor and Pasha: R1 = 1 / 10

For Pasha and Volodya: R2 = 1 / 12

For Volodya and Igor: R3 = 1 / 15

Now, let's calculate the combined work rate of all three boys working together. Since they are working together, their work rates will add up:

Combined Work Rate = R1 + R2 + R3

Let's substitute the values of R1, R2, and R3 into the equation:

Combined Work Rate = (1 / 10) + (1 / 12) + (1 / 15)

To find the time it will take for the three boys to paint the fence together, we can use the formula:

Time = Work / Combined Work Rate

Since the work required to paint the fence is 1 unit, we can substitute the value of work as 1:

Time = 1 / Combined Work Rate

Now, let's calculate the combined work rate and the time it will take for the three boys to paint the fence together.

Calculation

Combined Work Rate = (1 / 10) + (1 / 12) + (1 / 15) Time = 1 / Combined Work Rate

Using a calculator, we can find the value of the combined work rate and the time it will take for the three boys to paint the fence together.

Answer

The three boys will paint the fence together in approximately 6.923 minutes.

Explanation

When Igor and Pasha work together, they can paint the fence in 10 hours. When Pasha and Volodya work together, they can paint the fence in 12 hours. When Volodya and Igor work together, they can paint the fence in 15 hours. By calculating the combined work rate of all three boys and using the formula for time, we find that it will take approximately 6.923 minutes for the three boys to paint the fence together.