Question

Катер прошел 15 км против течения реки, затратив на весь путь столько же времени, сколько ему потребовалось бы, если бы он шел 22 км по озеру. Какова собственная скорость катера, если известно, что скорость течения реки 2 км/ч? Помоги срочно пожалуйста

Answer 1

Ответ:

6 2/7 км/ч

Объяснение:

Пусть собственная скорость катера х км/ч, тогда скорость против течения х-2 км/ч. Составим уравнения:

15/(х-2) = 22/х

15х=22(х-2)

15х=22х-44

7х=44

х=44/7=6 2/7

Answer 2

Объяснение:

15/(х-2)=22/х

15х=22(х-2)

15х=22х-44

22х-15х=44

7х=44

х=44:7

х=6 2/7

Answer 3

Problem Analysis

We are given that a boat traveled 15 km against the current of a river and took the same amount of time as it would have taken to travel 22 km on a lake. We are also given that the speed of the river's current is 2 km/h. We need to find the speed of the boat.

Solution

Let's assume the speed of the boat is x km/h.

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. Therefore, the boat's effective speed is (x - 2) km/h.

We can use the formula speed = distance / time to calculate the time taken for each leg of the journey.

For the journey against the current: - Distance = 15 km - Speed = (x - 2) km/h - Time = 15 / (x - 2) hours

For the journey on the lake: - Distance = 22 km - Speed = x km/h - Time = 22 / x hours

According to the given information, the time taken for both journeys is the same. Therefore, we can set up the following equation:

15 / (x - 2) = 22 / x

To solve this equation, we can cross-multiply and simplify:

15x = 22(x - 2) 15x = 22x - 44 7x = 44 x = 44 / 7 x ≈ 6.29

Therefore, the speed of the boat is approximately 6.29 km/h.

Answer

The speed of the boat is approximately 6.29 km/h.