Question

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

Answer 1

Пусть х км/ч собственная скорость лодки

2(х+3) км проплыла лодка по течению

3(х-3) км проплала лодка против течения, т.к. расстояния равны, получаем:

3(х-3) = 2(х+3)

3х - 9 = 2х + 6

3х - 2х = 6 + 9

х = 15

Ответ. 15 км/ч собственная скорость лодки.

Answer 2

Problem Analysis

We are given that a motorboat takes 2 hours to travel a certain distance with the current of a river and 3 hours to travel the same distance against the current of the river. We need to find the speed of the motorboat when there is no current, given that the speed of the river current is 3 km/h.

Solution

Let's assume the speed of the motorboat in still water is x km/h.

When the motorboat is traveling with the current, its effective speed is the sum of its own speed and the speed of the current. Therefore, the effective speed is x + 3 km/h.

Similarly, when the motorboat is traveling against the current, its effective speed is the difference between its own speed and the speed of the current. Therefore, the effective speed is x - 3 km/h.

We are given that the motorboat takes 2 hours to travel a certain distance with the current and 3 hours to travel the same distance against the current. Let's denote the distance as d km.

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

1. When traveling with the current: (x + 3) = d/2 (Equation 1) 2. When traveling against the current: (x - 3) = d/3 (Equation 2)

We can solve this system of equations to find the value of x, which represents the speed of the motorboat in still water.

Solving the Equations

Let's solve the system of equations (Equation 1 and Equation 2) to find the value of x.

From Equation 1, we have x + 3 = d/2. From Equation 2, we have x - 3 = d/3.

We can rewrite Equation 1 as x = d/2 - 3 and Equation 2 as x = d/3 + 3.

Setting the right-hand sides of the two equations equal to each other, we have:

d/2 - 3 = d/3 + 3

Now, we can solve this equation for d.

Calculating the Value of d

To solve the equation d/2 - 3 = d/3 + 3 for d, we can start by multiplying both sides of the equation by 6 to eliminate the denominators:

6 * (d/2 - 3) = 6 * (d/3 + 3)

Simplifying, we get:

3d - 18 = 2d + 18

Next, we can isolate d by subtracting 2d from both sides of the equation:

3d - 2d - 18 = 2d - 2d + 18

Simplifying further, we have:

d - 18 = 18

Finally, we can solve for d by adding 18 to both sides of the equation:

d - 18 + 18 = 18 + 18

Simplifying, we get:

d = 36

Therefore, the distance d is 36 km.

Calculating the Speed of the Motorboat

Now that we know the distance d is 36 km, we can substitute this value back into either Equation 1 or Equation 2 to solve for x, the speed of the motorboat in still water.

Let's use Equation 1: x + 3 = d/2.

Substituting d = 36, we have:

x + 3 = 36/2

Simplifying, we get:

x + 3 = 18

Finally, we can solve for x by subtracting 3 from both sides of the equation:

x + 3 - 3 = 18 - 3

Simplifying, we have:

x = 15

Therefore, the speed of the motorboat in still water is 15 km/h.

Answer

The speed of the motorboat in still water is 15 km/h.

Verification

To verify our answer, let's check if it satisfies the given conditions.

When the motorboat is traveling with the current at a speed of 15 km/h, its effective speed is 15 + 3 = 18 km/h. It takes 2 hours to travel a distance of 36 km, which is consistent with the given information.

Similarly, when the motorboat is traveling against the current at a speed of 15 km/h, its effective speed is 15 - 3 = 12 km/h. It takes 3 hours to travel the same distance of 36 km, which is also consistent with the given information.

Therefore, our answer of 15 km/h for the speed of the motorboat in still water is verified.

Conclusion

The speed of the motorboat in still water is 15 km/h.