Question

Катер по течению за 6 ч. проплыл такое же расстояние, которое проплывает за 8 ч. против течения. Скорость течения реки равна 3 км/ч. Вычисли скорость катера в стоячей воде.

Answer 1

Пусть Х-это скорость в стоячей воде
Х+3 -это скорость по течению
Х-3 -это скорость против течения
Решение:
(X+3)×6=(X-3)×8
6X+18=8X-24
6X-8X=-24-18
-2X=-42
X=-42÷(-2)
X=21
Ответ: 21 км/часэто скорость катера в стоячей воде.

Answer 2

Calculating the Speed of the Boat in Still Water

To calculate the speed of the boat in still water, we can use the following formula:

Speed of boat in still water = (Speed downstream + Speed upstream) / 2

Where: - Speed downstream = Speed of the boat with the current - Speed upstream = Speed of the boat against the current

First, let's calculate the speed of the boat with the current and against the current using the given information.

Calculating Speed of the Boat with the Current

The boat travels the same distance downstream in 6 hours as it does upstream in 8 hours. The speed of the current is 3 km/h.

Using the formula: Distance = Speed × Time

Let's denote the speed of the boat in still water as B and the distance traveled as D.

For the downstream journey: - Distance = 6 hours × (B + 3 km/h) = 6(B + 3) km

For the upstream journey: - Distance = 8 hours × (B - 3 km/h) = 8(B - 3) km

Since the distances are the same: 6(B + 3) = 8(B - 3)

Now, let's solve for B.

6B + 18 = 8B - 24 2B = 42 B = 21 km/h

So, the speed of the boat with the current is 21 km/h.

Calculating Speed of the Boat against the Current

Now, let's calculate the speed of the boat against the current.

The speed of the boat against the current is the difference between the speed of the boat in still water and the speed of the current: Speed upstream = 21 km/h - 3 km/h = 18 km/h

Calculating Speed of the Boat in Still Water

Now, using the formula: Speed of boat in still water = (21 km/h + 18 km/h) / 2 = 39 / 2 = 19.5 km/h

So, the speed of the boat in still water is 19.5 km/h.

Answer 3

Problem Analysis

We are given that a boat travels the same distance in 6 hours downstream as it does in 8 hours upstream. The speed of the river current is given as 3 km/h. We need to calculate 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 downstream, 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, 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 8 hours. Using the formula distance = speed × time, we can set up the following equation:

(x + 3) × 6 = (x - 3) × 8

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

Calculation

Expanding the equation:

6x + 18 = 8x - 24

Rearranging the terms:

6x - 8x = -24 - 18

-2x = -42

Dividing both sides by -2:

x = 21

Answer

The speed of the boat in still water is 21 km/h.

Explanation

When the boat is traveling downstream at a speed of 21 km/h (its speed in still water), the effective speed is 21 km/h + 3 km/h (speed of the current) = 24 km/h. In 6 hours, the boat covers a distance of 24 km/h × 6 hours = 144 km downstream.

Similarly, when the boat is traveling upstream at a speed of 21 km/h, the effective speed is 21 km/h - 3 km/h = 18 km/h. In 8 hours, the boat covers a distance of 18 km/h × 8 hours = 144 km upstream.

Therefore, the boat covers the same distance of 144 km both downstream and upstream, as given in the problem statement.