Question

Расстояние 210 км катер проходит по течении реки на 4 ч быстрее,чем против течения.Определите собственную скорость катера,если известно,что скорость течения реки равна 3км\ч очень надо решите задачу и квадратное уровнение

Answer 1

210/(x + 3) + 4 = 210/(x -3)

Answer 2

Problem Analysis

We are given that a boat travels a distance of 210 km. The boat travels 4 hours faster downstream (with the current) than upstream (against the current). The speed of the current is given as 3 km/h. We need to determine the speed of the boat.

Solution

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

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's speed downstream is (x + 3) km/h.

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat's speed upstream is (x - 3) km/h.

We are given that the boat takes 4 hours less time to travel downstream than upstream. This can be expressed as the following equation:

210 / (x + 3) = 210 / (x - 3) + 4

To solve this equation, we can cross-multiply and simplify:

210(x - 3) = 210(x + 3) + 4(x + 3)(x - 3)

Simplifying further:

210x - 630 = 210x + 630 + 4(x^2 - 9)

Simplifying again:

210x - 630 = 210x + 630 + 4x^2 - 36

Combining like terms:

4x^2 - 36 = 1260

Dividing both sides by 4:

x^2 - 9 = 315

Rearranging the equation:

x^2 = 324

Taking the square root of both sides:

x = ±18

Since the speed of the boat cannot be negative, we can conclude that the speed of the boat in still water is 18 km/h.

Answer

The speed of the boat in still water is 18 km/h.