Question

ПО ДЕЙСТВИЯ моторная лодка проходит расстояние между двумя пристанями А и В по течению реки за 6ч , а против течения за 8 ч . Скорость течения реки равна 3 км/ч . Како во расстояние между двумя пристанями . Определите собственную скорость лодки . ПОМОГИТЕ ПОЖАЛУЙСТА

Answer 1

Пусть х км/час скорость лодки,
(х+3) км/час скорость по течению,  (х+3)*6 км прошла по течению
(х-3) км/час протои течения, (х-3)*8 км прошла против течения. составим уравнение.
(х+3)*6=(х-3)*8
6х+18=8х+24
14х=42
х=3 км/час собственная скорость лодки
3+3=6 км/час скорость лодки по течению реки
6*6=36 км расстояние от пункта А до В.

Answer 2

Problem Analysis

We are given that a motorboat travels a certain distance between two docks, A and B, along a river. The boat takes 6 hours to travel from A to B with the current and 8 hours to travel from B to A against the current. The speed of the river current is given as 3 km/h. We need to determine the distance between the two docks and the speed of the motorboat.

Solution

Let's assume the speed of the motorboat is x km/h.

When the motorboat is traveling with the current, its effective speed is the sum of its own speed and the speed of the current. Therefore, the effective speed is (x + 3) km/h.

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

We can use the formula speed = distance / time to calculate the distance between the two docks.

When the motorboat is traveling with the current: distance = (x + 3) km/h * 6 hours.

When the motorboat is traveling against the current: distance = (x - 3) km/h * 8 hours.

Since the distance between the two docks is the same in both cases, we can equate the two distances and solve for x.

Calculation

Let's calculate the distance between the two docks and the speed of the motorboat.

When the motorboat is traveling with the current: distance = (x + 3) km/h * 6 hours.

When the motorboat is traveling against the current: distance = (x - 3) km/h * 8 hours.

Setting the two distances equal to each other: (x + 3) km/h * 6 hours = (x - 3) km/h * 8 hours.

Simplifying the equation: 6x + 18 = 8x - 24.

Solving for x: 2x = 42, x = 21.

Therefore, the speed of the motorboat is 21 km/h.

To find the distance between the two docks, we can substitute the value of x into either of the distance formulas.

Using the formula when the motorboat is traveling with the current: distance = (21 + 3) km/h * 6 hours, distance = 24 km/h * 6 hours, distance = 144 km.

Therefore, the distance between the two docks is 144 km.

Answer

The distance between the two docks, A and B, is 144 km. The speed of the motorboat is 21 km/h.