Question

Катер по течению за 6 ч. проплыл такое же расстояние, которое проплывает за 7 ч. против течения. Скорость течения реки равна 3 км/ч. Вычисли скорость катера в стоячей воде. Скорость катера в стоячей воде равна ____ км/ч. Сколько километров по течению проплыл катер? ____ км.

Answer 1

Ответ:

пусть искомая скорость х, тогда 6*(х+3)=7*(х-3) или 6*х+18=7*х-21 или х=21+18=39 км/час скорость в стоячей воде. Катер проплыл 6*42+7*36=504 км.

Answer 2

Problem Analysis

We are given that a boat travels the same distance in 6 hours downstream as it does in 7 hours upstream. The speed of the river's current is given as 3 km/h. We need to calculate the speed of the boat in still water and the distance traveled downstream.

Calculation

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

When the boat is traveling downstream, it gets a boost from the current, so its effective speed is the sum of its speed in still water and the speed of the current. Therefore, the boat's speed downstream is (x + 3) km/h.

When the boat is traveling upstream, it has to overcome the resistance of the current, so its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the boat's speed upstream is (x - 3) km/h.

We are given that the boat travels the same distance downstream in 6 hours as it does upstream in 7 hours. Let's denote the distance traveled as d km.

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

For downstream: (x + 3) = d / 6 (Equation 1)

For upstream: (x - 3) = d / 7 (Equation 2)

To solve for x, we can solve these two equations simultaneously.

Solution

Let's solve the equations:

From Equation 1, we have: x + 3 = d / 6

From Equation 2, we have: x - 3 = d / 7

Adding these two equations together, we get: 2x = (d / 6) + (d / 7)

To simplify the equation, we can find a common denominator: 2x = (7d + 6d) / (6 * 7)

Simplifying further, we have: 2x = (13d) / 42

Dividing both sides by 2, we get: x = (13d) / (2 * 42)

Simplifying, we have: x = (13d) / 84 (Equation 3)

Now, let's calculate the distance traveled downstream.

From Equation 1, we have: x + 3 = d / 6

Substituting the value of x from Equation 3, we get: (13d) / 84 + 3 = d / 6

To simplify the equation, we can find a common denominator: (13d + 252) / 84 = d / 6

Cross-multiplying, we have: 6(13d + 252) = 84d

Expanding and simplifying, we get: 78d + 1512 = 84d

Subtracting 78d from both sides, we have: 1512 = 6d

Dividing both sides by 6, we get: d = 252

Therefore, the distance traveled downstream is 252 km.

Now, let's calculate the speed of the boat in still water.

Substituting the value of d into Equation 3, we have: x = (13 * 252) / 84

Simplifying, we get: x = 39

Therefore, the speed of the boat in still water is 39 km/h.

Answer

The speed of the boat in still water is 39 km/h. The boat traveled 252 km downstream.

Note: The calculations and solution provided above are based on the given information and assumptions.