Question

Игорь и паша красят забор за 3 часа паша и володя красят этот же забор за 4 часа а володя и игорь за 6 часов за сколько минут мальчики покрасят забор работая вторем?

Answer 1

И + П = 3 ч
П + В = 4 ч
В + И = 6 ч
Весь объём работы принимаем за целое (1) :
1) 1 : 3 = 1/3 забора - красят И+П за 1 ч
2) 1 : 4 = 1/4 забора - красят П+В за 1 ч
3) 1 : 6 = 1/6 забора - красят В+И за 1 ч
4) (1/3 + 1/4 + 1/6) : 2  = (4/12 + 3/12 + 2/12) : 2  = 9/12 : 2 = 3/4 : 2 = 3/4 * 1/2 = 3/8 забора - покрасят Игорь, Паша и Володя вместе за 1 ч
5) 1 : 3/8 = 1 * 8/3 = 8/3 = 2 2/3 ч = 2 ч 40 мин. - 160 минут - покрасят вместе весь забор  ответ.

Answer 2

Problem Analysis

We are given the following information: - Igor and Pasha can paint a fence in 3 hours. - Pasha and Volodya can paint the same fence in 4 hours. - Volodya and Igor can paint the same fence in 6 hours.

We need to determine how many minutes it will take for the boys to paint the fence if they work 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 boys to paint the fence together, we can set up the following equations:

- Igor's work rate: 1 fence / 3 hours = 1/180 fence per minute - Pasha's work rate: 1 fence / 3 hours = 1/180 fence per minute - Volodya's work rate: 1 fence / 4 hours = 1/240 fence per minute

Since the boys are working together, their work rates will add up. Therefore, we can set up the equation:

(1/180 + 1/180 + 1/240) * x = 1 fence

Simplifying the equation:

(3/540 + 3/540 + 2/540) * x = 1 fence (8/540) * x = 1 fence x = (540/8) minutes x = 67.5 minutes

Therefore, it will take the boys 67.5 minutes to paint the fence together.

Answer

The boys will take 67.5 minutes to paint the fence together.