Question

Помогите пожалуйста!!!! Моторная лодка плыла 1,8 ч. по течению реки, затем 1,2 ч. по озеру. Скорость течения реки 2,8 км/ч. Найдите собственную скорость моторной лодки, если ее средняя скорость равна 33,68 км/ч.

Answer 1

Problem Analysis

We are given the following information: - The motorboat traveled for 1.8 hours along the river current. - The motorboat then traveled for 1.2 hours on the lake. - The speed of the river current is 2.8 km/h. - The average speed of the motorboat is 33.68 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 along the river current, its effective speed is the difference between its speed in still water and the speed of the river current. So, the effective speed is (x - 2.8) km/h.

The motorboat traveled for 1.8 hours along the river current, so the distance covered is 1.8 * (x - 2.8) km.

When the motorboat is traveling on the lake, its speed is the sum of its speed in still water and the speed of the river current. So, the speed is (x + 2.8) km/h.

The motorboat traveled for 1.2 hours on the lake, so the distance covered is 1.2 * (x + 2.8) km.

The total distance covered by the motorboat is the sum of the distances covered along the river current and on the lake. This should be equal to the average speed multiplied by the total time taken.

Therefore, we have the equation:

1.8 * (x - 2.8) + 1.2 * (x + 2.8) = 33.68 * (1.8 + 1.2)

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:

1.8 * (x - 2.8) + 1.2 * (x + 2.8) = 33.68 * (1.8 + 1.2)

Simplifying the equation:

1.8x - 5.04 + 1.2x + 3.36 = 33.68 * 3

Combining like terms:

3x - 1.68 = 101.04

Adding 1.68 to both sides:

3x = 102.72

Dividing both sides by 3:

x = 34.24

Answer

The speed of the motorboat in still water is 34.24 km/h.

Please note that the given search results did not provide relevant information for this specific problem. The solution was derived using mathematical calculations.