Question

две бригады вспахали поле за 8 часов. за какое время может вспахаь поле каждая бригада работая самостаятельна если второй бригаде на это требуется на 12 ч большей чем первой

Answer 1

Пусть первая бригада может вспахать поле за х часов, вторая за (х+12) часов. За1 час первая бригада вспахивает 1/х часть поля, а вторая 1/(х+12) часть поля. Вместе за час они вспахивают (1/х+1/(х+3)) часть поля, она же равна 1/8 части поля. 
1/х+1/(х+12)=1/8, 
8*(х+12+х)=х*(х+12), 
x^2-4*x-96=0, 
(х-12)*(х+8)=0, 
х=12 или х=-8. 
По смыслу, х не может быть отрицательным, значит х=12. Первая бригада одна может вспахать поле за 12 часов, вторая за 24 часа.

Answer 2

Calculating Time for Each Brigade to Plow the Field Independently

To calculate the time it takes for each brigade to plow the field independently, we can use the following information:

- Two brigades plowed the field in 8 hours. - The second brigade takes 12 hours longer than the first brigade to plow the field independently.

Let's denote the time it takes for the first brigade to plow the field as x hours. According to the given information, the second brigade takes x + 12 hours to plow the field independently.

To find the time it takes for each brigade to plow the field independently, we can use the following equation:

1/x + 1/(x + 12) = 1/8

Solving this equation will give us the time it takes for each brigade to plow the field independently.

Calculation

Using the equation 1/x + 1/(x + 12) = 1/8, we can solve for x:

1/x + 1/(x + 12) = 1/8
```
```
[(x + 12) + x] / [x(x + 12)] = 1/8
```
```
(2x + 12) / (x^2 + 12x) = 1/8
```
```
8(2x + 12) = x^2 + 12x
```
```
16x + 96 = x^2 + 12x
```
```
0 = x^2 - 4x - 96

Using the quadratic formula, we can solve for x:

x = (-b ± √(b^2 - 4ac)) / (2a)
```
```
x = (-(-4) ± √((-4)^2 - 4*1*(-96))) / (2*1)
```
```
x = (4 ± √(16 + 384)) / 2
```
```
x = (4 ± √400) / 2
```
```
x = (4 ± 20) / 2
```
```
x = (4 + 20) / 2  or  x = (4 - 20) / 2
```
```
x = 24 / 2  or  x = -16 / 2
```
```
x = 12  or  x = -8

Since time cannot be negative, the first brigade takes 12 hours to plow the field independently. Therefore, the second brigade takes 12 + 12 = 24 hours to plow the field independently.

Conclusion

So, each brigade, working independently, can plow the field in: - 12 hours for the first brigade. - 24 hours for the second brigade.