Question

катер прошел 18 км по течению реки и 14 км против течения,затратив на весь путь 3ч 15 мин найти скорость течения если скорость катера 10км в час СРОЧНО

Answer 1

Ответ:

2 км/ч

Объяснение:

Собственная скорость катера = 10 км/ч

Скорость течения реки = х км/ч

Скорость катера по течению = 10 + х км/ч

Скорость катера против течения = 10 - х км/ч

3ч 15мин = 3ч + 15/60ч = 3ч + 1/4ч = 3. 1/4ч или 3,25ч

18/(10 + х) + 14/(10 - х) = 3,25

18 * (10 - х) + 14 * (10 + х) = 3,25 * (10 - х)*(10 + х)

180 - 18х + 140 + 14х = 3,25 * (100 + 10х - 10х - х²)

-4х + 320 = 3,25 * (100 - х²)

-4х + 320 = 325 - 3,25х²

-4х + 320 - 325 + 3,25х² = 0

3,25х² - 4х - 5 = 0

а = 3,25; в = -4; с = -5

Д = в² - 4ас

Д = (-4)² - 4 * 3,25 * (-5) = 16 + 65 = 81

√Д = √81 = 9

х1 = (-в-√Д)/2а

х1 = (4-9)/2*3,25 = -5/6,5

Не подходит, так как скорость не может иметь отрицательное значение

х2 = (-в+√Д)/2а

х2 = (4+9)/2*3,25 = 13/6,5 = 2

Скорость течения реки = (х) = 2 км/ч

Answer 2

Problem Analysis

We are given that a boat traveled 18 km downstream (with the current) and 14 km upstream (against the current) in a total time of 3 hours and 15 minutes. We need to find the speed of the current.

Solution

Let's assume the speed of the boat in still water is x km/h and the speed of the current is y 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 current. Therefore, the time taken to travel downstream is given by:

Time downstream = Distance downstream / Effective speed downstream

Similarly, when the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the time taken to travel upstream is given by:

Time upstream = Distance upstream / Effective speed upstream

We are given that the boat traveled 18 km downstream and 14 km upstream in a total time of 3 hours and 15 minutes, which is equivalent to 3.25 hours. Therefore, we can write the following equations:

18 / (x + y) + 14 / (x - y) = 3.25

Now, let's solve this equation to find the values of x and y.

Calculation

To solve the equation, we can use algebraic manipulation. Let's multiply the equation by (x + y)(x - y) to eliminate the denominators:

(18(x - y) + 14(x + y)) / ((x + y)(x - y)) = 3.25

Simplifying the equation:

18x - 18y + 14x + 14y = 3.25(x^2 - y^2)

Combining like terms:

32x - 4y = 3.25(x^2 - y^2)

Expanding the right side:

32x - 4y = 3.25x^2 - 3.25y^2

Rearranging the equation:

3.25x^2 - 32x + 3.25y^2 - 4y = 0

Now, we have a quadratic equation in terms of x and y. We can solve this equation to find the values of x and y.

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 3.25, b = -32, and c = 3.25y^2 - 4y.

Substituting the values:

x = (-(-32) ± √((-32)^2 - 4 * 3.25 * (3.25y^2 - 4y))) / (2 * 3.25)

Simplifying:

x = (32 ± √(1024 - 42.25(3.25y^2 - 4y))) / 6.5

Simplifying further:

x = (32 ± √(1024 - 13.8125y^2 + 17y)) / 6.5

Now, we can substitute the value of x into one of the original equations to solve for y.

Let's use the equation 18 / (x + y) + 14 / (x - y) = 3.25.

Substituting the value of x:

18 / ((32 ± √(1024 - 13.8125y^2 + 17y)) / 6.5 + y) + 14 / ((32 ± √(1024 - 13.8125y^2 + 17y)) / 6.5 - y) = 3.25

Simplifying this equation will give us the value of y, which is the speed of the current.

Answer

To find the speed of the current, we need to solve the equation 18 / ((32 ± √(1024 - 13.8125y^2 + 17y)) / 6.5 + y) + 14 / ((32 ± √(1024 - 13.8125y^2 + 17y)) / 6.5 - y) = 3.25.

Please note that the calculation involves solving a quadratic equation, which may result in multiple solutions. To find the correct solution, we need to substitute the values of x and y back into the original equation and verify if it satisfies the given conditions.

Unfortunately, the search results provided by You.com do not provide any relevant information to directly solve this problem. Therefore, we need to rely on the mathematical approach outlined above to find the solution.