Question

Лодочник проплыл 3 км по течению реки и 2 км против течения за то же время , за которое мог бы проплыть плот 3 км по течению. Собственная скорость лодки 2км/ч. Найдите скорость течения реки. Можно с таблицей, пожалуйста.

Answer 1

Х(км/ч)-скорость течения реки;х+2(км/ч)-скорость лодочника по течению;2-х(км/ч)-скорость против течения; 3/(2+х)(ч)-время лодочника по течению;2/(2-х)(ч)-время лодочника против течения.Составляем уравнение:3/(2+х) + 2/(2-х) = 3/х; (6-3х+4+2х)/(4-х²) = 3/х; (10-х)х=12-3х²; 10х-х²-12+3х²=0; 2х²+10х-12=0; х²+5х-6=0; Д=49; х₁=-6-не соотв.,х₂=1(км/ч)

Answer 2

Problem Analysis

We are given that a boatman traveled 3 km downstream and 2 km upstream in the same amount of time it would take a raft to travel 3 km downstream. The boat's speed is 2 km/h. We need to find the speed of the river's current.

Let's assume the speed of the river's current is x km/h.

Solution

To solve this problem, we can use the formula: speed = distance / time.

Let's calculate the time it takes for the boat to travel 3 km downstream: - Speed of the boat relative to the water = boat's speed + speed of the current = 2 km/h + x km/h = (2 + x) km/h. - Distance = 3 km. - Time = Distance / Speed = 3 km / (2 + x) km/h.

Now, let's calculate the time it takes for the boat to travel 2 km upstream: - Speed of the boat relative to the water = boat's speed - speed of the current = 2 km/h - x km/h = (2 - x) km/h. - Distance = 2 km. - Time = Distance / Speed = 2 km / (2 - x) km/h.

Since the boat traveled the same distance downstream and upstream in the same amount of time, we can set up the following equation:

3 km / (2 + x) km/h = 2 km / (2 - x) km/h.

To solve this equation, we can cross-multiply:

3 km * (2 - x) km/h = 2 km * (2 + x) km/h.

Simplifying the equation:

6 - 3x = 4 + 2x.

Rearranging the equation:

5x = 2.

Solving for x:

x = 2/5 km/h.

Therefore, the speed of the river's current is 2/5 km/h.

Answer

The speed of the river's current is 2/5 km/h.