Question

Длина поля прямоугольной формы на 500 метров больше его ширины . Фермер шагая с одинаковой скоростью проходит поле по его длине за 40 мин , а по ширине за 30 мин . Чему равна площадь этого поля ?

Answer 1

40-30=10ммин эту разницу в 10 минут  фермер проходит 500 метров 

500:10=50  м/мин  скорость фермера

50*40=2000 м или 2км - длина поля

2000-500=1500м  или =1,5км-ширина поля

1,5*2=3(км2) - площадь поля

Answer 2

a=x+500

 

b=x

 

v=(x+500)/40

v=x/30

 

приравниваем v

 

(x+500)/40= x/30

 

30х+15000=40х

 

10х=15000

х=1500 - ширина поля

1500+500=2000 - длина поля

 

1500*2000=3000000

 

Answer 3

Problem Analysis

We are given that the length of a rectangular field is 500 meters more than its width. The farmer takes 40 minutes to walk the length of the field and 30 minutes to walk the width of the field. We need to find the area of the field.

Solution

Let's assume the width of the field is x meters. According to the given information, the length of the field is 500 meters more than its width, so the length would be x + 500 meters.

To find the area of a rectangle, we multiply its length by its width. Therefore, the area of the field would be (x + 500) * x square meters.

Now, we need to find the value of x. We know that the farmer takes 40 minutes to walk the length of the field and 30 minutes to walk the width of the field. We can use the formula speed = distance / time to find the distance.

The speed of the farmer is the same for both the length and the width of the field. Therefore, we can set up the following equations:

speed = distance / time

For the length: speed = (x + 500) / 40

For the width: speed = x / 30

Since the speed is the same in both equations, we can equate them:

(x + 500) / 40 = x / 30

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

Calculation

Let's solve the equation to find the value of x:

(x + 500) / 40 = x / 30

To simplify the equation, we can cross-multiply:

30(x + 500) = 40x

Expanding the equation:

30x + 15000 = 40x

Subtracting 30x from both sides:

15000 = 10x

Dividing both sides by 10:

x = 1500

Answer

The width of the field is 1500 meters. Since the length is 500 meters more than the width, the length would be 1500 + 500 = 2000 meters.

To find the area of the field, we multiply the length by the width:

Area = Length * Width = 2000 * 1500 = 3,000,000 square meters.

Therefore, the area of the field is 3,000,000 square meters.