Question

4. Катер за 2 часа по озеру и за 3 часа против течения реки проплывает такое же расстояние, что за 3,4 ч по течению реки. Найдите собственную скорость катера, если скорость течения реки равна 2 км/ч. ПРОШУ ПОМОГИТЕ ЭТО СОЧ

Answer 1

Ответ:

8 км/ч.

Пошаговое объяснение:

Пусть собственная скорость катера х км/ч, тогда против течения его скорость равна (х - 2) км/ч, а по течению - (х + 2) км/ч.

Зная, что путь, пройденный по озеру и против течения реки, такой же, что при движении по течению, составим и решим уравнение:

2х + 3(х - ,2) = 3,4(х + 2)

2х + 3х - 6 = 3,4х + 6,8

2х + 3х - ,3,4х = 6+ 6,8

1,6х = 12,8

х = 12,8 : 1,6

х = 8

8 км/ч - собственная скорость катера.

Answer 2

Problem Analysis

We are given that a boat travels the same distance in 2 hours on a lake and in 3 hours against the current of a river. We are also given that the boat travels the same distance in 3.4 hours with the current of the river. We need to find the speed of the boat.

Solution

Let's assume the speed of the boat in still water is x km/h, and the speed of the river's current is 2 km/h.

When the boat is traveling with the current, its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's effective speed is (x + 2) km/h.

When the boat is traveling against the current, its effective speed is the difference between its own speed and 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 distance traveled by the boat in each scenario.

1. When the boat is traveling with the current: - Speed = (x + 2) km/h - Time = 3.4 hours - Distance = Speed * Time = (x + 2) * 3.4 km

2. When the boat is traveling against the current: - Speed = (x - 2) km/h - Time = 3 hours - Distance = Speed * Time = (x - 2) * 3 km

3. When the boat is traveling on the lake: - Speed = x km/h - Time = 2 hours - Distance = Speed * Time = x * 2 km

Since the boat travels the same distance in all three scenarios, we can set up the following equation:

(x + 2) * 3.4 = (x - 2) * 3 = x * 2

Now, let's solve this equation to find the value of x.

(x + 2) * 3.4 = (x - 2) * 3

Simplifying the equation:

3.4x + 6.8 = 3x - 6

Bringing like terms to one side:

3.4x - 3x = -6 - 6.8

Simplifying further:

0.4x = -12.8

Dividing both sides by 0.4:

x = -12.8 / 0.4

Calculating the value of x:

x = -32

Since speed cannot be negative, we can conclude that there is an error in the problem statement or the calculations. Please double-check the given information and try again.

If you have any further questions, please let me know.