Question

2 варіант Моторний човен пройшов 3 км за течією річки і 1 км проти течії, витративши на весьШлях 1 год. Знайти швидкість авна у стоячій воді, якщо швидкість течі річки дорівнює1 км/год.​

Answer 1

Ответ:

(2+√3) км/ч ≈3,7 км/ч

Пошаговое объяснение:

x - скорость моторной лодки, км/ч.

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

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

3x-3+x+1=x²-1

x²-1-4x+2=0

x²-4x+1=0; D=16-4=12

x₁=(4-2√3)/2=(2-√3) км/ч ≈2-1,7≈0,3 км/ч - этот корень не подходит:

1/(0,3-1)=1/(-0,7)=-1,4 ч

x₂=(4+2√3)/2=(2+√3) км/ч ≈2+1,7≈3,7 км/ч

Answer 2

Problem Analysis

We are given that a motorboat traveled 3 km downstream and 1 km upstream in a total of 1 hour. The speed of the river current is given as 1 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, its effective speed is the sum of its speed in still water and the speed of the river current. So, the effective speed downstream is (x + 1) km/h.

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the river current. So, the effective speed upstream is (x - 1) km/h.

We are given that the boat traveled 3 km downstream and 1 km upstream in a total of 1 hour. We can set up the following equation based on the time and distance traveled:

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

To solve this equation, we can multiply through by (x + 1)(x - 1) to eliminate the denominators:

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

Simplifying the equation:

3x - 3 + x + 1 = x^2 - 1

4x - 2 = x^2 - 1

Rearranging the equation:

x^2 - 4x + 1 = 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:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -4, and c = 1. Substituting these values into the quadratic formula:

x = (-(-4) ± √((-4)^2 - 4(1)(1))) / (2(1))

Simplifying:

x = (4 ± √(16 - 4)) / 2

x = (4 ± √12) / 2

x = (4 ± 2√3) / 2

x = 2 ± √3

Therefore, the speed of the boat in still water is 2 ± √3 km/h.

Answer

The speed of the boat in still water is 2 ± √3 km/h.