Question

За 8 часов лодка прошла по течению реки расстояние, в раза больше , чем за 5 часов против течения. Какова собственная скорость течения реки - 2 км/ч?

Answer 1

S = v * t - формула пути
х (км/ч) - собственная скорость лодки
х + 2 (км/ч) - скорость лодки по течению реки, t = 8 ч - время в пути
х - 2 (км/ч) - скорость лодки против течения реки, t = 5 ч - время в пути
Уравнение: (х + 2) * 8 = 2 * (х - 2) * 5
                    8х + 16 = 10х - 20
                    10х - 8х = 16 + 20
                    2х = 36
                    х = 36 : 2
                    х = 18
Ответ: 18 км/ч - собственная скорость лодки.

Проверка: (18 + 2) * 8 = 2 * (18 - 2) * 5
                   20 * 8 = 2 * 16 * 5
                   160 = 160 

Answer 2

Calculation of River Current Speed

To calculate the speed of the river current, we can use the given information about the boat's travel time and distances. Let's denote the boat's speed as B and the speed of the river current as C.

According to the problem statement, the boat traveled a distance that is x times greater than the distance it traveled against the current. We can set up the following equation:

8(B + C) = 5(B - C)

Simplifying the equation, we get:

8B + 8C = 5B - 5C

Combining like terms, we have:

3B = -13C

Now, we can solve for the ratio of the boat's speed to the river current's speed:

B/C = -13/3

Given that the river current's speed is 2 km/h, we can substitute this value into the equation to find the boat's speed:

B/2 = -13/3

Solving for B, we get:

B = -26/3

Therefore, the boat's speed is -26/3 km/h.

Please note that the negative sign indicates that the boat is traveling against the current.