Question

4. Лодка плыла против течения реки 3ч, а затем 1ч по озеру и всего проплыла 47 км. Какова собственная скорость лодки, если скорость течения реки 2км/ч?

Answer 1

Пусть  Vл скорость лодки, тогда по условию можно записать
(Vл-2)*3+Vл*1=47
3Vл-6+Vл=47
4Vл=53 ⇒ Vл= 13,25 км/ч

Answer 2

Problem Analysis

We are given the following information: - The boat traveled against the current of a river for 3 hours. - Then, it traveled on a lake for 1 hour. - The total distance traveled by the boat is 47 km. - The speed of the river's current is 2 km/h.

We need to find the boat's own speed.

Solution

Let's assume the boat's own speed is x km/h.

When the boat is traveling against the current of the river, its effective speed is reduced by the speed of the current. So, the boat's effective speed is (x - 2) km/h.

The boat traveled against the current for 3 hours, so the distance covered in this time is 3 * (x - 2) km.

After that, the boat traveled on the lake for 1 hour at its own speed, which is x km/h. So, the distance covered on the lake is 1 * x km.

The total distance traveled by the boat is given as 47 km. Therefore, we can write the equation:

3 * (x - 2) + 1 * x = 47

Simplifying the equation:

3x - 6 + x = 47

4x - 6 = 47

4x = 53

x = 53 / 4

x = 13.25 km/h

Therefore, the boat's own speed is 13.25 km/h.

Answer

The boat's own speed is 13.25 km/h.

Explanation

The boat traveled against the current of the river for 3 hours, covering a distance of 3 * (13.25 - 2) = 33.75 km. Then, it traveled on the lake for 1 hour, covering a distance of 1 * 13.25 = 13.25 km. The total distance traveled by the boat is 33.75 + 13.25 = 47 km, which matches the given information.