Question

Катер,собственная скорость которого 8км/ч,прошел по реке расстояние, равное 15 км по течению реки и такое же расстояние против течения. найдите скорость течения реки, если время, затраченное на весь путь, равно 4ч.

Answer 1

РЕШЕНИЕ СМОТРИ НА ФОТОГРАФИИ

Answer 2

Problem Analysis

We are given that a boat with a speed of 8 km/h traveled a distance of 15 km downstream and the same distance upstream. The total time taken for the entire journey is 4 hours. We need to find the speed of the river's current.

Solution

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

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. So, the effective speed is (8 + x) km/h.

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. So, the effective speed is (8 - 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 downstream is 15 km / (8 + x) km/h.

The time taken to travel upstream is 15 km / (8 - x) km/h.

According to the problem, the total time taken for the entire journey is 4 hours. So, we can write the equation:

(15 / (8 + x)) + (15 / (8 - x)) = 4

Now, we can solve this equation to find the value of x.

Calculation

Let's solve the equation:

(15 / (8 + x)) + (15 / (8 - x)) = 4

Multiplying both sides of the equation by (8 + x)(8 - x) to eliminate the denominators:

15(8 - x) + 15(8 + x) = 4(8 + x)(8 - x)

Simplifying the equation:

120 - 15x + 120 + 15x = 4(64 - x^2)

Combining like terms:

240 = 256 - 4x^2

Rearranging the equation:

4x^2 = 256 - 240

4x^2 = 16

Dividing both sides of the equation by 4:

x^2 = 4

Taking the square root of both sides:

x = ±2

Since the speed of the river's current cannot be negative, we can conclude that the speed of the river's current is 2 km/h.

Answer

The speed of the river's current is 2 km/h.