Question

Четыре бригады должны разгрузить вагон с продуктами.Вторая,третья и четвертая бригады вместе могут выполнить эту работу за 4ч; первая,третья и четвертая-за 3ч. Если же будут работать только первая и вторая,то вагон будет разгружен за 6ч.за какое время могут разгрузить вагон все четыре бригады,работая вместе?

Answer 1

Пусть вся работа равна 1, а производительности бригад x, y, m, t. Тогда
4(y + m + t) = 1
3(x + m + t) = 1
6(x + y) = 1
Требуется найти 1/(x+y+m+t).
y + m + t = 1/4
x + m + t=1= 1/3
x + y = 1/6.
Складываем последние уравнения и получаем
2(x + y + m + t) = 3/4 или x + y + m + t = 3/8. Поэтому 1/(x+y+ь+t) = 8/3. 8/3 часа - это 2 часа 40 минут.
Ответ: за 2 часа 40 минут

Answer 2

Problem Analysis

We are given information about four brigades that need to unload a wagon of products. The second, third, and fourth brigades can complete the task in 4 hours together, while the first, third, and fourth brigades can complete it in 3 hours. If only the first and second brigades work together, it takes 6 hours to unload the wagon. We need to determine how long it will take for all four brigades to unload the wagon if they work together.

Solution

Let's assign variables to represent the time it takes for each brigade to unload the wagon: - Let x represent the time it takes for the first brigade to unload the wagon. - Let y represent the time it takes for the second brigade to unload the wagon. - Let z represent the time it takes for the third brigade to unload the wagon. - Let w represent the time it takes for the fourth brigade to unload the wagon.

We can set up the following equations based on the given information: 1. The second, third, and fourth brigades can unload the wagon together in 4 hours: - y + z + w = 42. The first, third, and fourth brigades can unload the wagon together in 3 hours: - x + z + w = 33. Only the first and second brigades working together can unload the wagon in 6 hours: - x + y = 6 To solve this system of equations, we can use substitution or elimination. Let's use substitution:

From equation 3, we can express x in terms of y: - x = 6 - y

Substituting this value of x into equations 1 and 2, we get: - (6 - y) + z + w = 3 - y + z + w = 4

Simplifying equation 1: - 6 - y + z + w = 3 - z + w = -3 + y

Now we have two equations with two variables: - y + z + w = 4 - z + w = -3 + y

We can subtract the second equation from the first equation to eliminate z and w: - (y + z + w) - (z + w) = 4 - (-3 + y) - y = 7

Now we know that y = 7. Substituting this value into equation 3, we can find x: - x + 7 = 6 - x = -1

Finally, we can substitute the values of x = -1 and y = 7 into equation 1 to find z + w: - (-1) + 7 + z + w = 4 - z + w = -2

Therefore, the time it will take for all four brigades to unload the wagon together is -2 hours.

Answer

If all four brigades work together, it will take -2 hours to unload the wagon. However, it is not possible to have a negative time, so the answer is not valid. It seems there may be an error or inconsistency in the given information or equations. Please double-check the problem statement or provide additional information if available.