Question

Туристы проплыли на лодке по озеру 18 км за такое же время,что и 15 км против течения реки,впадающей в озеро.найдите скорость движения лодки по озеру,если скорость течения реки 2 км\ч Задача11:13

Answer 1

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 that flows into the lake. The speed of the river's current is given as 2 km/h. We need to find the speed of the boat on the lake.

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 its speed and the speed of the river's current. Therefore, the effective speed of the boat on the lake is (x + 2) km/h.

We are 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. We can set up the following equation based on the concept of speed = distance/time:

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

To solve this equation, we can cross-multiply and then solve for x:

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

Simplifying the equation:

18x - 36 = 15x + 30

18x - 15x = 30 + 36

3x = 66

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.