Question

Игорь и Паша красят забор за 6 часов. Паша и Володя красят этот же забор за 7 часов, а Володя и Игорь — за 14 часов. За сколько минут мальчики покрасят забор, работая втроём?

Answer 1

Игорь+Паша=1/35
Паша+Володя=1/40
Володя+Игорь=1/56 
приводим все к такому уравнению :1/35+1/40+1/56=20/280 => 1/14 переворачиваем и умножаем на 2 
Ответ: 28

Answer 2

И+П=1/35П+В=1/40В+И=1/56 приводим все к такому уравнению :1/35+1/40+1/56=20/280 => 1/14 переворачиваем и умножаем на 2 Ответ: 28

Answer 3

Problem Analysis

We are given information about the time it takes for different pairs of boys to paint a fence. Igor and Pasha can paint the fence in 6 hours, Pasha and Volodya can paint it in 7 hours, and Volodya and Igor can paint it in 14 hours. We need to determine how long it will take for all 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 let the work rate of Igor be represented by I, the work rate of Pasha be represented by P, and the work rate of Volodya be represented by V, then we can set up the following equations:

1. Igor and Pasha can paint the fence in 6 hours, so their combined work rate is I + P = 1/6. 2. Pasha and Volodya can paint the fence in 7 hours, so their combined work rate is P + V = 1/7. 3. Volodya and Igor can paint the fence in 14 hours, so their combined work rate is V + I = 1/14.

We can solve these equations to find the individual work rates of each boy. Adding the three equations together, we get:

(I + P) + (P + V) + (V + I) = 1/6 + 1/7 + 1/14

Simplifying the equation, we have:

2(I + P + V) = 7/42 + 6/42 + 3/42

2(I + P + V) = 16/42

I + P + V = 8/42

I + P + V = 4/21

Now, we know that the combined work rate of all three boys is 4/21. To find the time it will take for them to paint the fence together, we can use the formula:

Time = 1 / (I + P + V)

Substituting the value of I + P + V into the formula, we get:

Time = 1 / (4/21)

Simplifying the equation, we have:

Time = 21/4

Therefore, it will take the three boys 21/4 hours to paint the fence together.

Answer

The three boys will take 21/4 hours to paint the fence together when working as a team.