Question

C2. Игорь и Паша красят забор за 6 часов. Паша и Володя красят этот же забор за 7 часов, а Володя и Игорь — за 21 час. За сколько минут мальчики покрасят забор, работая втроём?

Answer 1

1-вся работа

производительность И+П=1/6
производительность П+В=1/7
производительность В+И=1/21

сложим все эти производительность

И+П+П+В+В+И=1/6+1/7+1/21
2И+2П+2В=7/42+6/42+2/42
2(И+П+В)=15/42
И+П+В=15/42:2=15/42*1/2=15/84 -производительность всех троих
1:15/84=84/15=28/5=5,6ч=5ч 36мин=336мин -За столько минут мальчики покрасят забор, работая втроём

Answer 2

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 21 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 the amount of work done per unit of time. If we let x represent the time it takes for all three boys to paint the fence together, we can set up the following equations:

1. Igor and Pasha's work rate: (1/6) of the fence per hour 2. Pasha and Volodya's work rate: (1/7) of the fence per hour 3. Volodya and Igor's work rate: (1/21) of the fence per hour 4. All three boys' work rate: 1 fence per x hours

Since work rate is inversely proportional to time, we can add up the individual work rates to find the combined work rate:

(1/6) + (1/7) + (1/21) = 1/x

To solve for x, we can find the least common multiple (LCM) of the denominators of the fractions on the left side of the equation. In this case, the LCM of 6, 7, and 21 is 42. Multiplying both sides of the equation by 42, we get:

7 + 6 + 2 = 42/x

Simplifying, we have:

15 = 42/x

To solve for x, we can cross-multiply:

15x = 42

Dividing both sides by 15, we find:

x = 42/15 = 2.8 hours

Therefore, it will take the three boys approximately 2.8 hours to paint the fence together.

Answer

The three boys will paint the fence together in approximately 2.8 hours.