Question

Лодка может проплыть расстояние между двумя пунктами за 4 часа по течению и за 8 часов против течения.Скорость течения реки 2 км/ч.Найдитесобственную скорость лодки и расстояник между пунктами.

Answer 1

Пусть х км\ч - собственная скорость лодки

тогда (x+2) км\ч - скорость лодки по течению

(x-2)км\ч - скорость лодки против течения.

Т.к расстояние между пунктами не изменяется то получаем уравнения

(x+2)*4=(x-2)*8

находим что x=6

расстояние между пунктами: (6+2)*4=32км или (6-2)*8=32км

Ответ: 6 км/ч ; 32км

Answer 2

Problem Analysis

To solve this problem, we need to find the speed of the boat and the distance between the two points. We are given that the boat can travel the distance between the two points in 4 hours with the current and in 8 hours against the current. The speed of the current is given as 2 km/h.

Solution

Let's assume the speed of the boat in still water (without the current) is x 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 speed with the current 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 speed against the current is x - 2 km/h.

We are given that the boat can travel the distance between the two points in 4 hours with the current and in 8 hours against the current. Using the formula speed = distance / time, we can set up the following equations:

1. With the current: x + 2 = distance / 4 2. Against the current: x - 2 = distance / 8

To solve these equations, we can use the method of substitution. Rearranging equation 1, we get distance = (x + 2) * 4. Substituting this value into equation 2, we get:

(x - 2) = [(x + 2) * 4] / 8

Simplifying the equation:

x - 2 = (x + 2) / 2

Multiplying both sides by 2:

2x - 4 = x + 2

Simplifying further:

x = 6

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

To find the distance between the two points, we can substitute the value of x into one of the original equations. Let's use equation 1:

6 + 2 = distance / 4

Simplifying:

8 = distance / 4

Multiplying both sides by 4:

32 = distance

Therefore, the distance between the two points is 32 km.

Conclusion

The speed of the boat in still water is 6 km/h and the distance between the two points is 32 km.