Question

Решите задачу с помощью уравнения .катер прошел 5км по течению и 8км по озеру,затратив на весь путь 1ч.скорость течения реки равна 3км/ч .найдите скорость катера по течению ​

Answer 1

Пусть х  км/ час  - скорость катера по озеру

тогда ( х+3) км/ час  - скорость катера  по течению реки.

По условию катер   прошел 5км по течению реки, значит

затратил на этот путь  $\frac{5}{x+3}$  час.

и  катер   прошел 8км по озеру , затратил на этот путь  $\frac{8}{x}$  час.

На весь путь  катер затратил 1 час

Составляем уравнение               $\frac{5}{x+3}+\frac{8}{x}=1$

5x+8(x+3)=x(x+3)

x²-10x-24=0

D=100+96=196=14²

x₁=12;   x₂<0

12 км в час - скорость катера по озеру

12+3=15 км в час - скорость катера по течению

О т в е т. 15 км в час - скорость катера по течению

Answer 2

Problem Analysis

We are given that a boat traveled 5 km downstream (with the current) and 8 km on the lake, taking a total of 1 hour. 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 downstream (with the current), its effective speed is the sum of its speed in still water and the speed of the current. So, the effective speed downstream is (x + 3) km/h.

The time taken to travel downstream is given as 5 km, and we can use the formula time = distance / speed to find the time taken. Therefore, the time taken downstream is 5 / (x + 3) hours.

Similarly, when the boat is traveling on the lake (against the current), its effective speed is the difference between its speed in still water and the speed of the current. So, the effective speed on the lake is (x - 3) km/h.

The time taken to travel on the lake is given as 8 km, and we can use the formula time = distance / speed to find the time taken. Therefore, the time taken on the lake is 8 / (x - 3) hours.

Since the total time taken for the entire journey is given as 1 hour, we can add the times taken downstream and on the lake to get the equation:

(5 / (x + 3)) + (8 / (x - 3)) = 1

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

5(x - 3) + 8(x + 3) = (x + 3)(x - 3)

Simplifying the equation:

5x - 15 + 8x + 24 = x^2 - 9

Combining like terms:

13x + 9 = x^2 - 9

Rearranging the equation:

x^2 - 13x - 18 = 0

Now we can solve this quadratic equation to find the value of x, which represents the speed of the boat in still water.

Using the quadratic formula, where a = 1, b = -13, and c = -18:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values:

**x = (-(-13) ± √((-13)^2 - 4(1)(-18