Question

Длина водохранилища на 200км больше его ширины.Поездка на катере с одинаковой скоростью через водохранилище по его длине занимает 30ч а по ширине 20ч найди длину и ширину этого водохранилища с краткой записью пожалуйста

Answer 1

Problem Analysis

We are given that the length of a reservoir is 200 km greater than its width. The time it takes to travel across the reservoir at a constant speed is 30 hours along the length and 20 hours along the width. We need to find the length and width of the reservoir.

Solution

Let's assume the width of the reservoir is x km. According to the given information, the length of the reservoir is 200 km greater than its width, so the length can be represented as x + 200 km.

We are also given that the time it takes to travel across the reservoir at a constant speed is 30 hours along the length and 20 hours along the width.

To find the speed, we can use the formula:

Speed = Distance / Time

Let's calculate the speed along the length and width:

For the length: Speed along the length = (x + 200) km / 30 hours

For the width: Speed along the width = x km / 20 hours

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

(x + 200) km / 30 hours = x km / 20 hours

Now, let's solve this equation to find the value of x, which represents the width of the reservoir.

Calculation

To solve the equation, we can cross-multiply:

(x + 200) km * 20 hours = x km * 30 hours

Simplifying the equation:

20x + 4000 = 30x

Subtracting 20x from both sides:

4000 = 10x

Dividing both sides by 10:

x = 400

So, the width of the reservoir is 400 km.

Now, we can find the length of the reservoir by adding 200 km to the width:

Length = 400 km + 200 km = 600 km

Therefore, the length of the reservoir is 600 km and the width is 400 km.

Answer

The length of the reservoir is 600 km and the width is 400 km.