Question

Моторная лодка прошла 48км по течению реки и вернулась обратно,потратив на весь путь 7часов,Скорость речения реки равна 2км/. Найдите скорость лодке в неподвижной воде

Answer 1

Пусть х - собственная скорость лодки 

Тогда по течению скорость будет (х+2)

Против течения скорость (х-2) 

48/(х+2) + 48/(х-2) = 7

48·(х-2) + 48· (х+2) - 7·(х-2)·(х+2) =0 

 48х-96 +48х +96 -(7х-14) ·(х+2) =0 

96х - (7х²+14х -14х -28) =0

96х - 7х² -14х +14х +28=0

-7х²+96х +28=0

Д=10000

х=-2/7  и  х= 14

Отрицательное значение нам не подходит, поэтому берём только положительное.

 х=14 км/ч - собственная скорость лодки. Это и есть скорость в неподвижной воде, когда нет течения реки.

Answer 2

Problem Analysis

We are given that a motorboat traveled 48 km upstream on a river and then returned back, spending a total of 7 hours for the entire trip. The speed of the river current is given as 2 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, it is moving against the current, so its effective speed is reduced by the speed of the current. Therefore, the boat's speed upstream is (x - 2) km/h.

When the boat is traveling downstream, it is moving with the current, so its effective speed is increased by the speed of the current. Therefore, the boat's speed downstream is (x + 2) km/h.

We are given that the boat traveled 48 km upstream and then returned back, spending a total of 7 hours for the entire trip. We can set up the following equation based on the time and distance traveled:

48 / (x - 2) + 48 / (x + 2) = 7

To solve this equation, we can multiply both sides by (x - 2)(x + 2) to eliminate the denominators:

48(x + 2) + 48(x - 2) = 7(x - 2)(x + 2)

Simplifying the equation:

48x + 96 + 48x - 96 = 7(x^2 - 4)

96x = 7x^2 - 28

7x^2 - 96x - 28 = 0

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

Calculation

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation: 7x^2 - 96x - 28 = 0

a = 7, b = -96, c = -28

Substituting the values into the quadratic formula:

x = (-(-96) ± √((-96)^2 - 4 * 7 * (-28))) / (2 * 7)

Simplifying:

x = (96 ± √(9216 + 784)) / 14

x = (96 ± √9999) / 14

Calculating the square root of 9999:

√9999 ≈ 99.995

Substituting the value into the equation:

x = (96 ± 99.995) / 14

Calculating the two possible values of x:

x₁ = (96 + 99.995) / 14 ≈ 13.999

x₂ = (96 - 99.995) / 14 ≈ -0.285

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

Answer

The speed of the boat in still water is approximately 13.999 km/h.