Question

ОЧЕНЬ срочно пожалуймста!!!!!!!!!!!!!!!!!!!скорость лодки в стоячей воде 15 км/ч. лодка прошла 36 км против течения реки и 36 км по течению реки, затратив на весь путь 5 часов. найдите скорость течения реки

Answer 1

Ответ:

возможно если я неошибаюсь то 30

Answer 2

Problem Analysis

We are given that the speed of the boat in still water is 15 km/h. The boat travels 36 km against the current and 36 km with the current, taking a total of 5 hours for the entire journey. We need to find the speed of the river current.

Solution

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

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. So, the boat's speed against the current is (15 - x) km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So, the boat's speed with the current is (15 + x) km/h.

We can use the formula distance = speed × time to calculate the time taken for each leg of the journey.

The time taken to travel 36 km against the current is given by: 36 / (15 - x) hours.

The time taken to travel 36 km with the current is given by: 36 / (15 + x) hours.

According to the problem, the total time taken for the entire journey is 5 hours. So, we can write the equation:

36 / (15 - x) + 36 / (15 + x) = 5

To solve this equation, we can multiply through by the denominators to eliminate the fractions:

36(15 + x) + 36(15 - x) = 5(15 - x)(15 + x)

Simplifying the equation:

36(15 + x) + 36(15 - x) = 5(225 - x^2)

Expanding and simplifying further:

540 + 36x + 540 - 36x = 1125 - 5x^2

Combining like terms:

1080 = 1125 - 5x^2

Rearranging the equation:

5x^2 = 1125 - 1080

5x^2 = 45

Dividing both sides by 5:

x^2 = 9

Taking the square root of both sides:

x = ±3

Since the speed of the river current cannot be negative, the speed of the river current is 3 km/h.

Answer

The speed of the river current is 3 km/h.