Question

Тракторист должен вспахать поле площадью 180 га. Однако ежедневно он вспахивал на 2 га больше, чем планировал, и закончил работу на 1 день раньше, чем планировалось. За сколько дней тракторист вспахал поле?

Answer 1

Пусть х га тракторист дожен был вспахивать ежедневно. Тогда он бы вспахал 180 га за 180/x дней.
Но он вспахивал ежедневно по х+2 га и поэтому затратил 180/(х+2) дней.

$\frac{180}{x}-\frac{180}{x+2}=1 \\ \frac{180(x+2)-180x}{x(x+2)}=1$
180(x+2)-180x=x(x+2)
180x+360-180x=x²+2x
x²+2x-360=0
D=2²+4*360=4(1+360)=4*361
√D=√(4*361)=2*19=38
x₁=(-2-28)/2=-20 - посторонний корень
x₂=(-2+38)/2=18
Тракторист дожен был вспахивать 18 га в день, а вспахивал по 18+2=20 га в день. Поэтому он вспахал все поле за 180/20=9 дней

Answer 2

Calculation of Days to Plow the Field

To calculate the number of days it took the tractor driver to plow the field, we need to consider the following information:

- The planned area to plow was 180 hectares. - The tractor driver plowed 2 hectares more than planned each day. - The tractor driver finished the work 1 day earlier than planned.

To find the number of days it took to plow the field, we can set up an equation:

Let x be the number of days it took to plow the field.

The total area plowed can be calculated by multiplying the number of days by the additional area plowed each day:

Total area plowed = (x + 1) * (2 + x)

We can set up the equation:

180 = (x + 1) * (2 + x)

To solve this equation, we can expand and rearrange it:

180 = 2x + 2 + x^2 + x

Rearranging the equation:

x^2 + 3x + 2 - 180 = 0

Simplifying:

x^2 + 3x - 178 = 0

Now we can solve this quadratic equation to find the value of x.

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 3, and c = -178.

Plugging in the values:

x = (-3 ± √(3^2 - 4 * 1 * -178)) / (2 * 1)

Simplifying:

x = (-3 ± √(9 + 712)) / 2

x = (-3 ± √721) / 2

Since we are looking for a positive value for x, we can ignore the negative solution.

Calculating the square root of 721:

√721 ≈ 26.87

Plugging in the value:

x = (-3 + 26.87) / 2

x ≈ 23.87 / 2

x ≈ 11.94

Therefore, it took the tractor driver approximately 11.94 days to plow the field.

Please note that this calculation assumes a constant rate of plowing each day and does not account for any other factors that may affect the plowing process.