Question

Катер развивающий в стоячей воде скорость 20 км/ч прошел 36 км против течения и 22 км по течению затратив на весь путь 3 ч найдите скорость течения реки

Answer 1

х (км/ч)  -  скорость течения реки

(20 - х) км/ч  -  скорость катера против течения

(20 + х) км/ч  -  скорость катера по течению

Тогда время, затраченное на путь против течения равен:

36/(20 - x) ч

А время пути по течению реки:

22/(20 + x) ч

Составим уравнение:

36/(20 - x) + 22/(20 + x) = 3

36/(20 - x) + 22/(20 + x) - 3 = 0               x ≠ 20,  x ≠ - 20

720 + 36x + 440 - 22x - 3 * (20² - x²) = 0

1 160 + 14x - 1 200 + 3x² = 0

3x² + 14x - 40 = 0

D = 14² - 4 * 3 * (- 40) = 196 - (- 480) = 676

$x_{1}$ = $\tt\displaystyle\frac{-14+\sqrt{676}}{2*3}=\frac{-14+26}{6}=2$ км/ч

$x^{2}=$$\tt\displaystyle\frac{-14-\sqrt{676}}{2*3}=\frac{-14-26}{6}=-\frac{40}{6}$ - не подходит под условие

Ответ: скорость течения реки равна 2 км/ч.

Answer 2

Calculation of River Current Speed

To find the speed of the river current, we can use the formula:

Speed of boat in still water = Speed of boat against the current + Speed of current

Given information: - Speed of the boat in still water: 20 km/h - Distance traveled against the current: 36 km - Distance traveled with the current: 22 km - Total time taken: 3 hours

Let's calculate the speed of the river current using the given information.

1. Let's assume the speed of the river current as x km/h.

2. Speed of the boat against the current can be calculated using the formula:

Speed of boat against the current = Speed of boat in still water - Speed of current

Substituting the given values:

20 km/h - x km/h = 36 km / t1 where t1 is the time taken to travel against the current.

3. Speed of the boat with the current can be calculated using the same formula:

Speed of boat with the current = Speed of boat in still water + Speed of current

Substituting the given values:

20 km/h + x km/h = 22 km / t2 where t2 is the time taken to travel with the current.

4. We are given that the total time taken is 3 hours:

t1 + t2 = 3 hours

Now, we have a system of equations that we can solve to find the speed of the river current.

Let's solve the equations to find the value of x, which represents the speed of the river current.

Solution:

From equation 1: 20 km/h - x km/h = 36 km / t1

From equation 2: 20 km/h + x km/h = 22 km / t2

We can rearrange equation 1 to solve for t1:

t1 = 36 km / (20 km/h - x km/h)

Similarly, we can rearrange equation 2 to solve for t2:

t2 = 22 km / (20 km/h + x km/h)

Substituting these values into the equation t1 + t2 = 3 hours, we get:

36 km / (20 km/h - x km/h) + 22 km / (20 km/h + x km/h) = 3 hours

To solve this equation, we can multiply through by the denominators to eliminate the fractions:

36(20 km/h + x km/h) + 22(20 km/h - x km/h) = 3(20 km/h - x km/h)(20 km/h + x km/h)

Simplifying the equation:

720 km/h + 36x km + 440 km/h - 22x km = 3(400 km/h - x^2 km^2)

1160 km/h + 14x km = 1200 km/h - 3x^2 km^2

Rearranging the equation:

3x^2 km^2 + 14x km - 40 km/h = 0

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

Using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

where a = 3, b = 14, and c = -40.

Solving the equation, we get two possible values for x:

x ≈ 3.33 km/h or x ≈ -4.44 km/h

Since the speed of the river current cannot be negative, we can discard the negative value.

Therefore, the speed of the river current is approximately 3.33 km/h.

Please note that this calculation assumes a constant speed of the river current throughout the journey and does not take into account other factors that may affect the speed of the boat or the river current.

Let me know if you need any further assistance!