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 втроём.

Answer 1

И+П=10
В+П=12
В+И=15
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2(И+П+В) =37
разделим на 2 и получим полную чушь- втроем (18,5) дольше, чем попарно.
зайдем с другой стороны
Пр. труда И+П 1\10
Производительность труда П+В 1\12
Пр, тр. В+И=1\15
сложим производительности пар и сумму разделим пополам
1\10+1\12+1\15=(6+5+4)\60=15\60=1\4 1\4:2=1\8 берем обратное число и получаем похожий на правду ответ: за 8 часов втроем справятся.

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 let x represent the number of minutes it takes for the three boys to paint the fence together, we can set up the following equations:

- Igor's work rate: 1 fence / 10 hours = 1 fence / (10 * 60) minutes = 1/600 fences per minute - Pasha's work rate: 1 fence / 10 hours = 1 fence / (10 * 60) minutes = 1/600 fences per minute - Volodya's work rate: 1 fence / 12 hours = 1 fence / (12 * 60) minutes = 1/720 fences per minute

Since work rates add up when people work together, the combined work rate of the three boys is the sum of their individual work rates:

- Combined work rate: (1/600 + 1/600 + 1/720) fences per minute

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

- Time = 1 / Combined work rate

Let's calculate the time in minutes:

Calculation

The combined work rate is (1/600 + 1/600 + 1/720) fences per minute.

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

- Time = 1 / Combined work rate

Substituting the values, we get:

- Time = 1 / ((1/600) + (1/600) + (1/720)) minutes

Calculating this expression, we find that the three boys will paint the fence together in approximately 33.33 minutes.

Answer

Therefore, it will take the three boys approximately 33.33 minutes to paint the fence together.