Question

Задача. Човен за 5,2 год за течією річки пройшов на 2 км більше ніж проти течії за 6 год. Знайти власну швидкість човна, якщо швидкість течії 2,5 км/год.

Answer 1

х км/год - власна швидкість човна,  швидкість за течією х+2,5 км/год, проти течії х-2,5 км/год

5,2(х+2,5) - 6(х-2,5) = 2

5,2х+13-6х+15=2

0,8х=26;  х=26:0,8;  х=32,5

Відповідь:

32,5 км/год

Answer 2

Task Analysis

To solve this problem, we need to find the speed of the boat in still water given the speed of the river's current and the time it takes for the boat to travel a certain distance both with and against the current.

Given Information

- Boat's speed downstream (with the current): 5.2 hours to travel 2 km more than upstream (against the current) in 6 hours. - Speed of the river's current: 2.5 km/h.

Solution

Let's denote the speed of the boat in still water as b and the speed of the river's current as c.

Upstream and Downstream Speed Formulas

The speed of the boat downstream is the sum of the boat's speed in still water and the speed of the current: b + c

The speed of the boat upstream is the difference between the boat's speed in still water and the speed of the current: b - c

Equations

1. The boat's speed downstream: b + c 2. The boat's speed upstream: b - c 3. Distance traveled downstream: (b + c) * 5.2 4. Distance traveled upstream: (b - c) * 6

Equation from Given Information

From the given information, we have the equation: (b + c) * 5.2 = (b - c) * 6 + 2

Solving for b

Let's solve for b using the given equation and the provided values.

Calculation

Substitute the given values: (b + 2.5) * 5.2 = (b - 2.5) * 6 + 2

Expanding the equation: 5.2b + 13 = 6b - 15 + 2

Rearranging terms: 5.2b + 13 = 6b - 13

Solving for b: 6b - 5.2b = 13 + 13 0.8b = 26 b = 26 / 0.8 b = 32.5

Answer

The speed of the boat in still water is 32.5 km/h.