Question

Катер собственная скорость которого 8км/ч прошел по реке расстояния равное15 км по течению реки и такое же расстояние против течения. найдите скорость течения реки если время затраченное на весь путь равно 4 ч

Answer 1

1. 8 км/ч * 4 ч = 32 км - расстояние, пройденное катером с учётом скорости реки

2. 15 * 2 = 30 км - расстояние в оба конца без учёта скорости течения реки

3. 32 - 30 = 2 км /ч - скорость течения реки

Answer 2

Problem Analysis

We are given that a boat with a speed of 8 km/h traveled a distance of 15 km both upstream and downstream on a river. 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 (with the current), the effective speed of the boat will be the sum of its own speed and the speed of the current. So, the boat's effective speed downstream will be 8 + x km/h.

Similarly, when the boat is traveling upstream (against the current), the effective speed of the boat will be the difference between its own speed and the speed of the current. So, the boat's effective speed upstream will be 8 - x km/h.

We are given that the boat took a total of 4 hours to complete the entire journey (both upstream and downstream). Since the distance traveled upstream and downstream is the same (15 km), we can set up the following equation:

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

To solve this equation, we can multiply both sides 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)

240 = 256 - 4x^2

4x^2 = 16

x^2 = 4

Taking the square root of both sides:

x = 2

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

Answer

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