Question

Два друга работая вместе покрасили забор за 12 часов. Если бы 1 друг работал один он бы покрасил этот забор за 21 час. За сколько часов покрасил забор 2 друг работая 1?

Answer 1

Ответ:

1) 1 : 12 = 1/12 части забора — покрасят друг1 и друг2 за один час, так как весь забор они могут покрасить за 12 часов;

2) 1 : 21 = 1/21 части забора — покрасит друг 1 за один час, так как весь забор он может покрасить за 21 час;

3) 1/12 - 1/21 = 21/252 - 12/252 = 9/252 = 1/28 — покрасит друг 2за один час, так как друг 1и друг 2вместе покрасят 1/12 части забора за час;

4) 1 : 1/28 = 1 * 28 = 28 часов — покрасит забор друг2 работая один.

Ответ: за 28 часов.

Answer 2

Ответ:   28 часов.

Пошаговое объяснение:

Производительность первого равна 1/21 часть забора в час.

Пусть  второй красит забор за х часов.

Тогда его производительность равна 1/x часть  забора в час.

Общая производительность равна 1/12 часть  забора в час.

1/21+1/x=1/12;

12x+21*12=21x;

12x-21x=-252;

-9x=-252;

x=252:9;

x=28 часов необходимо второму для покраски забора

Answer 3

Problem Analysis

We are given that two friends painted a fence together in 12 hours. If one friend worked alone, they would have painted the fence in 21 hours. We need to determine how many hours it would take for the second friend to paint the fence if they worked alone.

Solution

Let's assume that the rate at which the first friend paints the fence is x units per hour. Therefore, the rate at which the second friend paints the fence is 1/21 units per hour, as they would take 21 hours to paint the fence alone.

When the two friends work together, their combined rate is x + 1/21 units per hour. We are given that they completed the job in 12 hours, so we can set up the following equation:

12(x + 1/21) = 1

Simplifying the equation:

12x + 12/21 = 1

Multiplying both sides of the equation by 21 to eliminate the fraction:

252x + 12 = 21

Subtracting 12 from both sides of the equation:

252x = 9

Dividing both sides of the equation by 252:

x = 9/252

Simplifying the fraction:

x = 1/28

Therefore, the rate at which the first friend paints the fence is 1/28 units per hour.

To find out how long it would take for the second friend to paint the fence alone, we need to determine their rate. Since the first friend's rate is 1/28 units per hour, the second friend's rate would be 1 - 1/28 = 27/28 units per hour.

Let's calculate the time it would take for the second friend to paint the fence alone using their rate:

Time = 1 / (27/28)

Simplifying the expression:

Time = 28/27

Therefore, it would take the second friend 28/27 hours to paint the fence alone.

Answer

If the first friend worked alone, they would have painted the fence in 21 hours. If the second friend worked alone, they would have painted the fence in 28/27 hours.