Question

Длина поля прямоугольной формы на 500м больше его ширины. Фермер, шагая с одинаковой скоростью, проходит поле по его длине за 40 минут. Чему равна площадь этого поля? (Выразите ответ в арах, в гектарах

Answer 1

Фермер, шагая с одинаковой скоростью, проходит поле по его длине за 40 минут, а по ширине - за 30 минут.
Пусть ширина поля х м, тогда скорость фермера х/30 м/мин. Длина поля (х+500) м,а его скорость (х+500)/40.
Составим и решим уравнение:
(х+500)/40=х/30
30х+15000=40х
10х=15000
х=1500 м ширина поля
1500+500=2000 м длина поля
S=1500*2000=3 000 000 м²
В арах и гектарах.
1 ар=100 м²
3000000:100=30 000 ар
1 га=10 000 м²
3 000 000:10 000=300 га
Ответ 30 000 ар или 300 га площадь поля

Answer 2

Problem Analysis

We are given that the length of a rectangular field is 500 meters more than its width. A farmer walks across the length of the field at a constant speed and takes 40 minutes to do so. We need to find the area of the field.

Solution

Let's assume the width of the field is x meters. According to the problem, the length of the field is 500 meters more than its width, so the length can be expressed as x + 500 meters.

To find the area of the field, we multiply the length by the width: Area = Length × Width.

Substituting the values, we get: Area = (x + 500) × x.

We know that the farmer takes 40 minutes to walk across the length of the field. We can use this information to find the speed of the farmer.

The speed of the farmer can be calculated using the formula: Speed = Distance / Time.

The distance the farmer walks is the length of the field, which is x + 500 meters. The time taken is 40 minutes, which is equal to 40/60 = 2/3 hours.

Substituting the values, we get: Speed = (x + 500) / (2/3).

Since the speed of the farmer is constant, we can equate the two expressions for speed:

(x + 500) / (2/3) = x / (40/60).

Simplifying the equation, we get: 3(x + 500) = 2x.

Solving for x, we find: x = 1500.

Now that we know the width of the field is 1500 meters, we can calculate the length: Length = x + 500 = 1500 + 500 = 2000 meters.

Finally, we can calculate the area of the field: Area = Length × Width = 2000 × 1500 = 3,000,000 square meters.

To express the area in hectares, we divide by 10,000 (since 1 hectare is equal to 10,000 square meters): Area in hectares = 3,000,000 / 10,000 = 300 hectares.

Therefore, the area of the field is 300 hectares.

Answer

The area of the rectangular field is 300 hectares.