Question

Катер прошел 14 км по течению и 20 км против течения, затратив на первый путь на 1 час меньше чем на второй. Скорость течения 2 км/ч. Найти собственную скорость катера.

Answer 1

Скорость       время       расстояние
Х+2                  t+1             14
X-2                   t                 20
Составляем уравнение
20     -   14     = 1
Х-2        Х+2

20*(Х+2) - 14*(Х-2) = 1* (Х+2)(Х-2)
20Х + 40 - 14Х + 28 = Х² - 4
Х² - 6Х -72 = 0
D= (b²-4*a*c)/2a
D= (-6)² - 4*1*(-72)=36 + 288 = 324
Х1= (-(-6)+√324)/2*1=(6+18)/2=24/2=12
Х2= (-(-6)-√324)/2*1=(6-18)/2=-12/2=-6 (не существует)
Ответ: собственная скорость катера 12 км/ч

Answer 2

Problem Analysis

We are given that a boat traveled 14 km downstream and 20 km upstream, taking 1 hour less for the downstream journey compared to the upstream journey. The speed of the current is given as 2 km/h. We need to find 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 took 1 hour less for the downstream journey compared to the upstream journey. This means that the time taken for the downstream journey is 1 hour less than the time taken for the upstream journey.

Using the formula time = distance / speed, we can set up the following equation:

14 / (x + 2) = 20 / (x - 2) - 1

Let's solve this equation to find the value of x.

Calculation

To solve the equation, we can start by cross-multiplying:

14(x - 2) = 20(x + 2) - (x + 2)

Simplifying the equation:

14x - 28 = 20x + 40 - x - 2

Combining like terms:

14x - 28 = 19x + 38

Moving all the terms to one side:

14x - 19x = 38 + 28

Simplifying:

-5x = 66

Dividing both sides by -5:

x = -66 / 5

So, the speed of the boat in still water is approximately -13.2 km/h.

Answer

The speed of the boat in still water is approximately -13.2 km/h.