Question

Моторная лодка за 2 ч. по течению реки проплывает такое же расстояние, как за 3 ч. против течения реки. Найдите собственную скорость лодки, если скорость течения реки равна 3 км/ч.

Answer 1

Х км/ч собственная скорость лодки, по течению скорость 3+х км/ч, против течения х-3  км\ч
расстояние по течению (х+3)2 км
расстояние против течения (х-3)3 км
 уравнение 
2( х+3)=3(х-3)
2х+6=3х-9
-х=-15
х=15 км/ч

Answer 2

Problem Analysis

We are given that a motorboat takes 2 hours to travel a certain distance downstream (with the current) and the same distance upstream (against the current) takes 3 hours. We need to find the speed of the boat if the speed of the river current is 3 km/h.

Solution

Let's assume the speed of the boat is B km/h. Since the boat is traveling downstream, its effective speed will be the sum of its own speed and the speed of the current. Therefore, the effective speed downstream is B + 3 km/h.

Similarly, when the boat is traveling upstream, its effective speed will be the difference between its own speed and the speed of the current. Therefore, the effective speed upstream is B - 3 km/h.

We are given that the boat takes 2 hours to travel the distance downstream and 3 hours to travel the same distance upstream. Let's denote the distance as D km.

Using the formula speed = distance / time, we can write the following equations:

Downstream: (B + 3) km/h = D km / 2 hours

Upstream: (B - 3) km/h = D km / 3 hours

To solve these equations, we can use the method of substitution. We can solve the first equation for D and substitute it into the second equation:

Downstream: D = (B + 3) km/h * 2 hours

Upstream: (B - 3) km/h = [(B + 3) km/h * 2 hours] / 3 hours

Now, let's solve for B.

Calculation

Downstream: D = (B + 3) km/h * 2 hours

Upstream: (B - 3) km/h = [(B + 3) km/h * 2 hours] / 3 hours

Simplifying the equations:

Downstream: D = 2B + 6 km

Upstream: 3(B - 3) = 2(B + 3)

Expanding and simplifying the equation:

3B - 9 = 2B + 6

B = 15 km/h

Answer

The speed of the boat is 15 km/h.