Question

2). Моторная лодка проплыла 15 км по течению реки и 21 км против течения, затратив на весь путь ч 20 мин. Какова скорость течения реки, если собственная скорость лодки равна 12 км/ч?

Answer 1

Ответ:

Пошаговое объяснение:

Я так понимаю, что на весь путь лодка затратила 1 ч 20 мин.

1 ч 20 мин = (1 20/60) ч = 4/3 ч

x - скорость течения реки, км/ч.

15/(12+x) +21/(12-x)=4/3

(15(12-x)+21(12+x))/((12+x)(12-x))=4/3

9(60-5x+84+7x)=4(144-x²)

9(144-2x)=4(144-x²)

648-9x-288+2x²=0

2x²-9x+360=0; D=81-2880=-2799; D<0 - уравнение не имеет решений.

Следовательно, задача при данном условии не имеет решений.

Answer 2

Calculation of River Current Speed

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

Speed of boat downstream - Speed of boat upstream = Speed of river current

Given that the boat traveled 15 km downstream and 21 km upstream, and the total time taken for the entire journey was 20 minutes, we can calculate the speed of the river current.

Let's denote the speed of the boat as B (12 km/h), the speed of the river current as C, and the time taken for the downstream journey as T1 and the upstream journey as T2.

The distance traveled downstream is 15 km, and the distance traveled upstream is 21 km. The total time taken for the entire journey is 20 minutes, which is equal to 1/3 of an hour.

Using the formula mentioned earlier, we can set up the following equations:

15 / (B + C) = T1 (Equation 1) 21 / (B - C) = T2 (Equation 2) T1 + T2 = 1/3 (Equation 3)

We can solve this system of equations to find the value of C, the speed of the river current.

Let's substitute the given values into the equations:

15 / (12 + C) = T1 21 / (12 - C) = T2 T1 + T2 = 1/3

Now, let's solve the equations:

From Equation 1, we can express T1 in terms of C: T1 = 15 / (12 + C)

From Equation 2, we can express T2 in terms of C: T2 = 21 / (12 - C)

Substituting the expressions for T1 and T2 into Equation 3, we get: 15 / (12 + C) + 21 / (12 - C) = 1/3

Simplifying the equation, we have: 45(12 - C) + 35(12 + C) = 4(12 + C)(12 - C)

Expanding and simplifying further: 540 - 45C + 420 + 35C = 48(12^2 - C^2)

Combining like terms: 960 = 48(144 - C^2)

Simplifying: 960 = 6912 - 48C^2

Rearranging the equation: 48C^2 = 5952

Dividing both sides by 48: C^2 = 124

Taking the square root of both sides: C = ±√124

Since the speed of the river current cannot be negative, we take the positive square root: C = √124

Calculating the square root of 124, we find that: C ≈ 11.14 km/h

Therefore, the speed of the river current is approximately 11.14 km/h.