Question

Срочнооооо!!!! Решите задачу с помощью уравнения катер прошел 5 км по течению реки и 8 км по озеру затратив на весь путь 1 час скорость течения реки равна 3 км ч Найдите скорость катера по течению​

Answer 1

Ответ:

Введем переменную, пусть собственная скорость катера равна х, значит, по озеру катер шел со скоростью х км/ч. А по течению реки катер шел со скоростью (х + 3) км/ч.

Выразим время движения катера по течению реки: t = S/v; 5/(х + 3).

Выразим время движения катера по озеру: 8/х.

Так на все он потратил 1 час, составляем уравнение:

5/(х + 3) + 8/х = 1;

(5х + 8х + 24)/х(х + 3) = 1;

(13х + 24)/(х² + 3х) = 1.

По правилу пропорции: х² + 3х = 13х + 24;

х² + 3х - 13х - 24 = 0;

х² - 10х - 24 = 0.

D = 100 + 96 = 196 (√D = 14);

х1 = (10 - 14)/2 = -2 (не подходит).

х2 = (10 + 14)/2 = 12 (км/ч) - собственная скорость катера.

Тогда скорость по течению будет равна х + 3 = 12 + 3 = 15 (км/ч).

Ответ: скорость катера по течению равна 15 км/ч.

Объяснение:

Answer 2

Problem Statement

We are given that a boat traveled 5 km upstream in a river and 8 km downstream in a lake, taking a total of 1 hour for the entire journey. The speed of the river current is given as 3 km/h. We need to find the speed of the boat in still water.

Solution

Let's assume the speed of the boat in still water is x km/h.

When the boat is traveling upstream (against the current), its effective speed is reduced by the speed of the current. So, the boat's speed relative to the ground is (x - 3) km/h.

Similarly, when the boat is traveling downstream (with the current), its effective speed is increased by the speed of the current. So, the boat's speed relative to the ground is (x + 3) km/h.

We are given that the boat traveled 5 km upstream and 8 km downstream, taking a total of 1 hour for the entire journey.

Using the formula distance = speed × time, we can write the following equations:

1. For the upstream journey: - Distance = 5 km - Speed = (x - 3) km/h - Time = Distance / Speed = 5 / (x - 3) hours

2. For the downstream journey: - Distance = 8 km - Speed = (x + 3) km/h - Time = Distance / Speed = 8 / (x + 3) hours

Since the total time for the entire journey is 1 hour, we can write the equation:

1 / (x - 3) + 1 / (x + 3) = 1

To solve this equation, we can multiply both sides by (x - 3)(x + 3) to eliminate the denominators:

(x + 3) + (x - 3) = (x - 3)(x + 3)

Simplifying the equation:

2x = x^2 - 9

Rearranging the equation:

x^2 - 2x - 9 = 0

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

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -2, and c = -9, we can substitute the values and solve for x.

Calculating the discriminant: b^2 - 4ac = (-2)^2 - 4(1)(-9) = 4 + 36 = 40

Since the discriminant is positive, we have two real solutions for x.

Using the quadratic formula:

x = (-(-2) ± √40) / (2 * 1) x = (2 ± √40) / 2 x = 1 ± √10

Therefore, the speed of the boat in still water can be either (1 + √10) km/h or (1 - √10) km/h.

Please note that the speed of the boat cannot be negative, so the valid solution is (1 + √10) km/h.

Answer

The speed of the boat in still water is (1 + √10) km/h.