Question

ПОМОГИТЕ РЕШИТЬ ЗАДАЧУ:От моста через реку поплыли пловец против течения и мяч по течениюЧерез 20 мин. пловец вспомнил о мяче, повурнул обратно и догнал его в 2 км от моста. Какова скорость течения? Я решить ее не могу, ПОМОГИТЕ!! Срочно!!

Answer 1

Если рассматривать движение пловца относительно воды, а не берега, то он плывет сначала в одну сторону 20 минут, а потом в другую еще 20 минут(скорость относительно воды не меняется).

Мяч за эти 40 минут проплыл 2 км.

Следовательно скорость течения V = 2км/⅔ часа = 3 км/час.

Answer 2

Problem Analysis

To solve this problem, we need to determine the speed of the current in the river. We are given that a swimmer swam against the current for 20 minutes and then turned back and caught a ball 2 km downstream from the starting point. We need to find the speed of the current.

Let's assume the speed of the swimmer in still water is S and the speed of the current is C.

Solution

1. When the swimmer is swimming against the current, their effective speed is reduced by the speed of the current. So, the effective speed of the swimmer is S - C. 2. In 20 minutes, the swimmer covers a distance equal to the effective speed multiplied by the time: (S - C) * 20 minutes. 3. When the swimmer turns back, they swim with the current, so their effective speed is increased by the speed of the current. The effective speed of the swimmer is now S + C. 4. The swimmer catches the ball 2 km downstream from the starting point, which means they covered a distance equal to the effective speed multiplied by the time it took to catch the ball: (S + C) * t. 5. Since the swimmer turned back after 20 minutes, the total time it took to catch the ball is 20 minutes plus the additional time t. 6. We can set up the following equation to solve for C: ``` (S - C) * 20 minutes = (S + C) * (20 minutes + t) ```

Let's solve this equation to find the speed of the current.

Solving the Equation

Expanding the equation, we get: ``` 20S - 20C = 20S + 20C + (S + C)t ``` Simplifying, we have: ``` -20C = (S + C)t ``` Dividing both sides by t, we get: ``` -20C/t = S + C ``` Rearranging the equation, we have: ``` C = -20C/t - S ``` Now, we can substitute the given values into the equation and solve for C.

Calculation

From the problem statement, we know that the swimmer caught the ball 2 km downstream from the starting point. Therefore, the distance covered by the swimmer with the current is 2 km. We also know that the swimmer turned back after 20 minutes.

Let's substitute these values into the equation: ``` C = -20C/20 - S C = -C - S 2C = -S C = -S/2 ```

Therefore, the speed of the current is equal to half the speed of the swimmer in still water, but in the opposite direction.

Answer

The speed of the current is equal to half the speed of the swimmer in still water, but in the opposite direction.

I hope this helps! Let me know if you have any further questions.