Question

Катер проплыл 24 км за течением реки и повернул назад, потратив на путь против течения на 1 час 4 минуты больше, чем на путь за течением. Найдите скорость течения, если собственная скорость катера равна 12 км\час.

Answer 1

х - скорость течения реки
24/(12-х) - 24/(12+х)=16/15     
24(12+х-12+х)=16(144-х²)/15

45(12+х-12+х)=2(144-х²)
45х=144-х²
х²+45х-144=0
х= - 22,5 +/- √(506,25+144)= -22,5 +25,5= 3 км/час скорость течения реки

Answer 2

Problem Analysis

We are given the following information: - The boat traveled 24 km downstream (with the current) and then returned upstream (against the current). - The time taken for the upstream journey was 1 hour and 4 minutes longer than the time taken for the downstream journey. - The speed of the boat is given as 12 km/h.

We need to find the speed of the current.

Solution

Let's assume the speed of the current is x km/h.

To solve this problem, we can use the formula: Speed = Distance / Time.

Let's calculate the time taken for the downstream journey: - Distance = 24 km - Speed of the boat = 12 km/h - Speed of the current = x km/h

The effective speed of the boat downstream is the sum of the boat's speed and the current's speed: (12 + x) km/h.

Using the formula, we can calculate the time taken for the downstream journey as follows: Time_downstream = Distance / Speed_downstream = 24 / (12 + x) hours. Now, let's calculate the time taken for the upstream journey: - Distance = 24 km - Speed of the boat = 12 km/h - Speed of the current = x km/h

The effective speed of the boat upstream is the difference between the boat's speed and the current's speed: (12 - x) km/h.

Using the formula, we can calculate the time taken for the upstream journey as follows: Time_upstream = Distance / Speed_upstream = 24 / (12 - x) hours. According to the problem, the time taken for the upstream journey is 1 hour and 4 minutes longer than the time taken for the downstream journey. We can convert 1 hour and 4 minutes to hours by dividing it by 60: (1 + 4/60) hours.

So, we have the equation: Time_upstream = Time_downstream + 1 + 4/60.

Substituting the values of Time_upstream and Time_downstream, we get: 24 / (12 - x) = 24 / (12 + x) + 1 + 4/60.

Now, let's solve this equation to find the value of x, which represents the speed of the current.

Calculation

To solve the equation, we can start by simplifying it:

24 / (12 - x) = 24 / (12 + x) + 1 + 4/60

Multiply both sides of the equation by (12 - x)(12 + x) to eliminate the denominators:

24(12 + x) = 24(12 - x) + (12 - x)(12 + x) + (12 - x)(4/60)(12 + x)

Simplifying further:

288 + 24x = 288 - 24x + 144 - x^2 + (4/60)(144 - x^2)

Simplifying the right side:

288 + 24x = 288 - 24x + 144 - x^2 + (4/60)(144 - x^2)

288 + 24x = 288 - 24x + 144 - x^2 + (2/15)(144 - x^2)

Multiplying both sides by 15 to eliminate the fraction:

4320 + 360x = 4320 - 360x + 2160 - 15x^2 + 2(144 - x^2)

Simplifying further:

4320 + 360x = 4320 - 360x + 2160 - 15x^2 + 288 - 2x^2

Combining like terms:

360x = -15x^2 + 288 - 2x^2

0 = -17x^2 + 288

17x^2 = 288

Dividing both sides by 17:

x^2 = 288 / 17

Taking the square root of both sides:

x = sqrt(288 / 17)

Evaluating the square root:

x ≈ 4.69 km/h

Therefore, the speed of the current is approximately 4.69 km/h.

Answer

The speed of the current is approximately 4.69 km/h.