Question

Катер за 2 часа по течению реки проходит на 8 км больше, чем за это время против течения. Найдите скорость течения реки, если собственная скорость катера 15 км/ч.

Answer 1

x–скорость течения реки

3(25–x)–2(25+x)=5

75–3x–50–2x=5

–5x=–20

x=4

Ответ: скорость течения реки 4 км/ч

Answer 2

Ответ:

2×(15+x)-2×(15-x)=8

30+2x-30+2x=8

4x=8

x=8÷4

x=2 км/ч скорость течения реки

Answer 3

Problem Analysis

We are given that a boat travels 8 km more in 2 hours with the current than against the current. We need to find the speed of the current if the boat's own speed is 15 km/h.

Solution

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

When the boat is traveling with the current, its effective speed is the sum of its own speed and the speed of the current. So, the boat's effective speed is 15 + x km/h.

When the boat is traveling against the current, its effective speed is the difference between its own speed and the speed of the current. So, the boat's effective speed is 15 - x km/h.

According to the problem, the boat travels 8 km more in 2 hours with the current than against the current. We can set up the following equation:

2(15 + x) = 2(15 - x) + 8

Let's solve this equation to find the value of x.

Equation Solution

Expanding the equation, we get:

30 + 2x = 30 - 2x + 8

Simplifying the equation, we get:

4x = 8

Dividing both sides of the equation by 4, we get:

x = 2

Answer

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

Explanation

When the boat is traveling with the current at a speed of 15 km/h, the effective speed is 15 + 2 = 17 km/h. In 2 hours, the boat will travel a distance of 17 * 2 = 34 km.

When the boat is traveling against the current at a speed of 15 km/h, the effective speed is 15 - 2 = 13 km/h. In 2 hours, the boat will travel a distance of 13 * 2 = 26 km.

The boat travels 8 km more with the current than against the current, which matches the given information.

Conclusion

The speed of the current is 2 km/h.