Question

Туристы проплыли на лодке по озеру 18 км за такое же время ,что и 15 км против течения реки впадающего в в озеро.Найти скорость движения лодки по озеру ,если скорость течения реки 2 км/ч

Answer 1

Скорость лодки в стоячей воде Vкм/час; Тогда ее скорость в реке против течения : (V-2)км/час; Ввиду того, что время движения во всех средах одинаково составим уравнение: V/18км=(V-2)/15км; Решаем уравнение: 15V=18V-36; Откуда : 3V=36; V=12км/час; Ответ:скорость лодки по озеру 12км/час.

Answer 2

Problem Analysis

We are given that tourists traveled by boat on a lake for a distance of 18 km in the same amount of time it took them to travel 15 km against the current of a river flowing into the lake. We need to find the speed of the boat on the lake, given that the speed of the river current is 2 km/h.

Solution

Let's assume the speed of the boat on the lake is x km/h. Since the boat is traveling with the current of the river on the lake, the effective speed of the boat will be the sum of the boat's speed and the speed of the river current. Therefore, the effective speed of the boat on the lake is x + 2 km/h.

We are also given that the boat traveled a distance of 18 km on the lake in the same amount of time it took to travel 15 km against the current of the river. This means that the time taken for both distances is equal.

To find the time taken, we can use the formula:

Time = Distance / Speed

Let's calculate the time taken to travel 18 km on the lake and 15 km against the current of the river.

For the distance of 18 km on the lake: Time1 = 18 / (x + 2)

For the distance of 15 km against the current of the river: Time2 = 15 / (x - 2)

Since both times are equal, we can set up the following equation:

18 / (x + 2) = 15 / (x - 2)

To solve this equation, we can cross-multiply and simplify:

18(x - 2) = 15(x + 2)

Expanding and simplifying:

18x - 36 = 15x + 30

Bringing like terms to one side:

18x - 15x = 30 + 36

Simplifying further:

3x = 66

Dividing both sides by 3:

x = 22

Therefore, the speed of the boat on the lake is 22 km/h.

Answer

The speed of the boat on the lake is 22 km/h.