Question

Моторная лодка проплыла по течению 4 часа, против течения – 3 часа. Путь, пройденный по течению, на 27 км больше пути против течения. Найдите скорость лодки в стоячей воде, если скорость течения равна 2,5 км/ч. помогите пожалуйста​

Answer 1

Пусть х км/ч - собственная скорость лодки, тогда (х + 2,5) км/ч - скорость лодки по течению реки, (х - 2,5) км/ч - скорость лодки против течения реки. Путь по течению на 27 км больше. Уравнение:

(х + 2,5) · 4 - (х - 2,5) · 3 = 27

4х + 10 - 3х + 7,5 = 27

4х - 3х = 27 - 10 - 7,5

х = 9,5

Ответ: 9,5 км/ч.

Answer 2

Problem Analysis

We are given the following information: - The motorboat traveled with the current for 4 hours. - The motorboat traveled against the current for 3 hours. - The distance traveled with the current is 27 km more than the distance traveled against the current. - The speed of the current is 2.5 km/h.

We need to find the speed of the motorboat in still water.

Solution

Let's assume the speed of the motorboat in still water is x km/h.

When the motorboat is traveling with the current, its effective speed is the sum of its speed in still water and the speed of the current. Therefore, the distance traveled with the current can be calculated as:

Distance with current = (Speed with current) × (Time with current)

Substituting the given values, we have:

Distance with current = (x + 2.5) × 4

Similarly, when the motorboat is traveling against the current, its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the distance traveled against the current can be calculated as:

Distance against current = (Speed against current) × (Time against current)

Substituting the given values, we have:

Distance against current = (x - 2.5) × 3

We are also given that the distance traveled with the current is 27 km more than the distance traveled against the current. Mathematically, we can express this as:

Distance with current = Distance against current + 27

Substituting the previously calculated values, we have:

(x + 2.5) × 4 = (x - 2.5) × 3 + 27

Now, we can solve this equation to find the value of x, which represents the speed of the motorboat in still water.

Calculation

Let's solve the equation step by step:

(x + 2.5) × 4 = (x - 2.5) × 3 + 27

Expanding the equation:

4x + 10 = 3x - 7.5 + 27

Combining like terms:

4x - 3x = 27 - 7.5 - 10

Simplifying:

x = 9.5

Answer

The speed of the motorboat in still water is 9.5 km/h.

Explanation

When the motorboat is traveling with the current, its effective speed is the sum of its speed in still water and the speed of the current. Therefore, the distance traveled with the current is greater than the distance traveled against the current. In this case, the difference in distance is 27 km.

By solving the equation, we find that the speed of the motorboat in still water is 9.5 km/h. This means that when there is no current, the motorboat can travel at a speed of 9.5 km/h.