Question

В 10:00 туристы на лодке поплыли из пункта А вниз по течению реки. Пройдя 12 километров, туристы остановились для отдыха на 3 часа. Затем они вернулись в пункт А в 18:00. Определить (в км/час) собственную скорость лодки, если скорость течения реки 1 км/час

Answer 1

18-10-3=5ч
12/(х+1)+12/(х-1)=5
12х-12+12х+12=5х^2-5
5x^2-24x-5=0
x1=-0.2 - не удовлетворяет
x2=5км/ч скорость лодки

Answer 2

Problem Analysis

The problem states that tourists on a boat started their journey from point A at 10:00 AM, traveling downstream along a river. After covering a distance of 12 kilometers, they stopped for a 3-hour break and then returned to point A by 6:00 PM. We need to determine the speed of the boat in kilometers per hour, given that the speed of the river's current is 1 kilometer per hour.

Solution

To solve this problem, we can use the concept of relative speed. The speed of the boat with respect to the river's current is the difference between the speed of the boat and the speed of the current. When the boat is traveling downstream, the speed of the boat with respect to the ground is the sum of the speed of the boat and the speed of the current. Similarly, when the boat is traveling upstream, the speed of the boat with respect to the ground is the difference between the speed of the boat and the speed of the current.

Let's denote the speed of the boat as B km/h and the speed of the current as C km/h. Since the boat is traveling downstream, the speed of the boat with respect to the ground is B + C km/h. The time taken to cover a distance of 12 kilometers downstream is given as 8 hours (from 10:00 AM to 6:00 PM).

Using the formula: distance = speed × time, we can write the equation as: 12 = (B + C) × 8

Simplifying the equation, we get: B + C = 12/8 B + C = 1.5

Now, let's consider the time taken for the return journey. The boat is traveling upstream, so the speed of the boat with respect to the ground is B - C km/h. The time taken to cover a distance of 12 kilometers upstream is 3 hours.

Using the formula: distance = speed × time, we can write the equation as: 12 = (B - C) × 3

Simplifying the equation, we get: B - C = 12/3 B - C = 4

We now have a system of equations: B + C = 1.5 B - C = 4

Adding the two equations, we can eliminate the variable C: 2B = 5.5

Solving for B, we find: B = 5.5/2 B = 2.75 km/h

Therefore, the speed of the boat is 2.75 kilometers per hour.

Answer

The speed of the boat is 2.75 kilometers per hour.

Explanation

The tourists started their journey at 10:00 AM and traveled downstream for 8 hours, covering a distance of 12 kilometers. After a 3-hour break, they returned to point A by 6:00 PM. The speed of the river's current is 1 kilometer per hour. By solving the system of equations, we determined that the speed of the boat is 2.75 kilometers per hour.