Question

Длина поля прямоугольной формы на 500 м больше его ширины.фермер,шагая с одинаковой скоросьью,проходит поле по его длине за 40минут,а по ширине-за 30минут.чему равна площадь этого поля?

Answer 1

Х - ширина
х+500 - длина 

х/30=(х+500)/40
40х=30*(х+500)
40х=30х+15000
10х=15000
х=1500 м - ширина
х+500=1500+500=2000 м - длина 
1500*2000=3 000 000 м² -  площадь этого поля

в км
1500 м=1,5 км - ширина
2000 м=2 км - длина 
1,5*2=3 км² -  площадь этого поля

Answer 2

Finding the Dimensions of the Field

To find the dimensions of the field, we can set up a system of equations based on the given information. Let's denote the length of the field as L and the width as W.

Given: - The length of the field is 500m longer than its width: L = W + 500. - The farmer walks the length of the field in 40 minutes and the width in 30 minutes.

Calculating the Dimensions

We can use the formula: distance = speed × time to calculate the dimensions of the field.

The speed of the farmer is constant, so we can use the formula to calculate the dimensions of the field.

Let's denote the speed of the farmer as S.

- For the length of the field: L = S × 40 (since the farmer walks the length in 40 minutes). - For the width of the field: W = S × 30 (since the farmer walks the width in 30 minutes).

Solving for the Dimensions

We can solve the system of equations to find the values of L and W.

From the given information: - L = W + 500 - L = 40S - W = 30S

By substituting the values of L and W from the second and third equations into the first equation, we get: 40S = 30S + 500

Solving for S: 40S - 30S = 500 10S = 500 S = 50

Now that we have the value of S, we can find the dimensions of the field: L = 40S = 40 × 50 = 2000m W = 30S = 30 × 50 = 1500m

Calculating the Area of the Field

Now that we have the dimensions of the field, we can calculate its area using the formula: Area = Length × Width

Substituting the values: Area = 2000m × 1500m = 3,000,000 square meters

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