Question

Расстояние от пристони A до пристани В катер по течению реки проплыл за 6 ч.а от пристони В до пристани А- за 7 ч. Скорость течения реки 2 км/ч. Найдите собственную скорость катера. Нужно решить уравнением

Answer 1

Собственная скорость катера х км ч. скорость по течению  х+2, против течениях-2
6*(х+2)=7*(х-2) 
х=26

Answer 2

Problem Analysis

We are given that a boat traveled from port A to port B downstream in 6 hours, and from port B to port A upstream in 7 hours. The river current has a speed of 2 km/h. We need to find 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 from A to B, it benefits from the river current, so the effective speed is the sum of the boat's speed and the current's speed. Therefore, the boat's effective speed is (x + 2) km/h.

When the boat is traveling upstream from B to A, it has to overcome the river current, so the effective speed is the difference between the boat's speed and the current's speed. Therefore, the boat's effective speed is (x - 2) km/h.

We can use the formula distance = speed × time to calculate the distances traveled in each direction.

The distance from A to B is the same as the distance from B to A. Let's call this distance d km.

Using the formula, we can write the following equations:

1. Distance from A to B: (x + 2) × 6 = d 2. Distance from B to A: (x - 2) × 7 = d

We can solve this system of equations to find the value of x.

Let's solve the equations step by step:

1. Expand the equations: - Equation 1: 6x + 12 = d - Equation 2: 7x - 14 = d

2. Since both equations are equal to d, we can set them equal to each other: - 6x + 12 = 7x - 14

3. Simplify the equation: - 12 + 14 = 7x - 6x - 26 = x

Therefore, the speed of the boat in still water is 26 km/h.

Answer

The speed of the boat in still water is 26 km/h.