Question

Катер по течению за 3 ч. проплыл такое же расстояние, которое проплывает за 6 ч. против течения. Скорость течения реки равна 2 км/ч. Вычисли скорость катера в стоячей воде.

Answer 1

Скорость катера в стоячей воде - это собственная скорость
катера (Vс).

По течению:
S =  t  (Vc+Vт) , где  t = 3 ч. ,  Vт= 2 км/ч
S= 3 (Vc+2)

Против течения:
S= t (Vc - Vт)  ,  где  t= 6 ч. , Vт = 2 км/ч
S= 6(Vc -2) 

Расстояние, которое катер прошел по течению и против течения, одинаковое. ⇒ Уравнение.
3(Vc +2 ) = 6 (Vc-2)
3Vc +6 = 6Vc -12
3Vc - 6Vc  = -12-6
-3Vc=-18 
3Vc=18
Vc = 18÷3
Vc= 6  км/ч   - собственная скорость катера.
Проверим:
3* (6+2) =3*8= 24 км - расстояние
6*(6-2) = 6*4=24 км - расстояние 

Ответ: 6 км/ч скорость катера в стоячей воде.

Answer 2

Problem Analysis

We are given that a boat travels the same distance in 3 hours downstream (with the current) as it does in 6 hours upstream (against the current). The speed of the river current is given as 2 km/h. We need to calculate the speed of the boat in still water.

Solution

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

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current. So, the effective speed downstream is (x + 2) km/h.

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. So, the effective speed upstream is (x - 2) km/h.

We are given that the boat travels the same distance downstream in 3 hours as it does upstream in 6 hours. Using the formula speed = distance / time, we can set up the following equations:

Downstream: Distance = Speed * Time Distance = (x + 2) * 3

Upstream: Distance = Speed * Time Distance = (x - 2) * 6

Since the distances are the same, we can equate the two equations:

(x + 2) * 3 = (x - 2) * 6

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

Calculation

Expanding the equation:

3x + 6 = 6x - 12

Rearranging the terms:

6x - 3x = 12 + 6

3x = 18

Dividing both sides by 3:

x = 6

Answer

The speed of the boat in still water is 6 km/h.

Explanation

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current, which is 6 + 2 = 8 km/h. In 3 hours, the boat covers a distance of 8 km/h * 3 hours = 24 km downstream.

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current, which is 6 - 2 = 4 km/h. In 6 hours, the boat covers a distance of 4 km/h * 6 hours = 24 km upstream.

Therefore, the boat covers the same distance of 24 km both downstream and upstream, as given in the problem statement.