Question

Помогите пожалуйста решить задачу. Моторная лодка за 4 часа проходит по течению реки тот же путь, что и за 6 часов против течения реки. Определите собственную скорость лодки, если скорость течения равна 3 км./ч.

Answer 1

4( Х + 3 ) = 6( Х - 3 )
4х + 12 = 6х - 18
2х = 30
Х = 15 ( км/час ) собственная скорость лодки

Answer 2

Problem Analysis

We are given that a motorboat takes 4 hours to travel a certain distance with the current of a river, and it takes 6 hours to travel the same distance against the current of the river. We need to determine the speed of the boat in still water.

Solution

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

When the boat is traveling with the current, its effective speed is the sum of its speed in still water and the speed of the current. So, the effective speed is (x + 3) km/h.

When the boat is traveling against the current, its effective speed is the difference between its speed in still water and the speed of the current. So, the effective speed is (x - 3) km/h.

We can use the formula distance = speed × time to set up two equations based on the given information:

1. When the boat is traveling with the current: - Distance = (x + 3) km/h × 4 hours

2. When the boat is traveling against the current: - Distance = (x - 3) km/h × 6 hours

Since the distance traveled in both cases is the same, we can set up the following equation:

(x + 3) × 4 = (x - 3) × 6

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

Calculation

Expanding the equation:

4x + 12 = 6x - 18

Rearranging the terms:

4x - 6x = -18 - 12

-2x = -30

Dividing both sides by -2:

x = -30 / -2

x = 15

Answer

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

Please let me know if I can help you with anything else.