Question

Из двух пунктов реки расстояние между которыми равно 51 км, навстречу друг другу движутся две моторные лодки, собственная скорость каждой из которых равна 15 км/ч. До встречи лодка, идущая по течению, шла 1,5 ч, а лодка идущая против течения шла 2 ч. Найдите скорость течения реки

Answer 1

Х (км/ч) - собственная скорость моторной лодки (одинаковая)
  х + 3 (км/ч) - скорость лодки по течению реки
  х - 3 (км/ч) - скорость лодки против течения реки
 (х + 3) * 1,5 + (х - 3) * 2 = 51 
 1,5х + 4,5 + 2х - 6 = 51
 1,5х + 2х = 51 - 4,5 + 6 
 3,5х = 52,5   
 х = 52,5 : 3,5
 х = 15 (км/ч) - собственная скорость моторной лодки
Ответ:15 км\ч

Answer 2

Х км/ч - скорость течения
15+х  км/ч - скорость лодки по течению
15-х  км/ч - скорость другой лодки, против течения
1,5(15+х) км - прошла первая лодка
2(15-х)  км - прошла вторая лодка
Расстояние 51 км

1,5(15+х)+2(15-х)=51
22,5+1,5х+30-2х=51
0,5х=1,5
х=1,5:0,5
х=3(км/ч)-скорость течения

Answer 3

Problem Analysis

We have two motorboats moving towards each other on a river. The distance between them is 51 km. The speed of each boat is 15 km/h. One boat has been traveling for 1.5 hours, while the other boat has been traveling for 2 hours. We need to find the speed of the river's current.

Solution

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

The boat moving downstream (with the current) has been traveling for 1.5 hours, so the distance it has covered is 15 * 1.5 = 22.5 km.

The boat moving upstream (against the current) has been traveling for 2 hours, so the distance it has covered is 15 * 2 = 30 km.

The total distance between the two boats is 51 km. Therefore, the sum of the distances covered by the two boats should be equal to 51 km:

22.5 km + 30 km = 51 km

Now, let's consider the effect of the river's current on the boats' speeds.

The boat moving downstream is aided by the current, so its effective speed is the sum of its own speed and the speed of the current:

15 km/h + x km/h = 15 + x km/h

The boat moving upstream is hindered by the current, so its effective speed is the difference between its own speed and the speed of the current:

15 km/h - x km/h = 15 - x km/h

Since the time taken by both boats is the same (they are moving towards each other), we can set up the following equation:

22.5 km / (15 + x km/h) = 30 km / (15 - x km/h)

Now, let's solve this equation to find the value of x.

Calculation

To solve the equation, we can cross-multiply:

22.5 km * (15 - x km/h) = 30 km * (15 + x km/h)

Simplifying further:

337.5 - 22.5x = 450 + 30x

Combining like terms:

52.5x = 112.5

Dividing both sides by 52.5:

x = 112.5 / 52.5

Calculating the value of x:

x ≈ 2.14 km/h

Answer

The speed of the river's current is approximately 2.14 km/h.