Question

Катер проходит определённое расстояние в стоячей воде за 12 ч. То же расстояние он может пройти по течению за 10 ч. Против течения катер идёт со скоростью 24 км/ч. Определите скорость катера по течению.РЕШИТЬ С ПОМОЩЬЮ ПРОПОРЦИЙ.

Answer 1

(S/12)/(S/10)=(Vk)/(Vk+Vт) => Vk=5*Vт
24=Vk-Vт => 24=5*Vт-Vт => Vт=6 => Vk=5*Vт=30 => Vk+Vт=30+6=36 - ответ

Answer 2

Problem Analysis

We are given that a boat travels a certain distance in still water in 12 hours. The same distance can be covered downstream in 10 hours. We are also given that the boat travels against the current at a speed of 24 km/h. We need to determine the speed of the boat in still water.

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, the effective speed is the sum of the boat's speed in still water and the speed of the current. So, the effective speed is (x + y) km/h.

According to the given information, the boat covers the distance in still water in 12 hours and the same distance downstream in 10 hours. Using the formula speed = distance / time, we can set up the following equations:

1. Distance in still water = (x km/h) * (12 hours) 2. Distance downstream = (x + y km/h) * (10 hours)

Since the distances are the same, we can equate the two equations:

(x km/h) * (12 hours) = (x + y km/h) * (10 hours)

Simplifying the equation:

12x = 10(x + y)

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

Let's solve the equation step by step:

12x = 10(x + y) (Equation 1)

Expanding the equation:

12x = 10x + 10y

Combining like terms:

12x - 10x = 10y

2x = 10y

Dividing both sides by 2:

x = 5y

So, the speed of the boat in still water is 5 times the speed of the current.

Now, we are given that the boat travels against the current at a speed of 24 km/h. This means that the effective speed is the difference between the boat's speed in still water and the speed of the current. So, the effective speed is (x - y) km/h.

According to the given information, the boat covers the same distance upstream in 12 hours. Using the formula speed = distance / time, we can set up the following equation:

Distance upstream = (x - y km/h) * (12 hours)

Since the distances are the same, we can equate this equation to the distance in still water:

(x km/h) * (12 hours) = (x - y km/h) * (12 hours)

Simplifying the equation:

12x = 12(x - y)

Now, we can solve this equation to find the value of y, which represents the speed of the current.

Let's solve the equation step by step:

12x = 12(x - y) (Equation 2)

Expanding the equation:

12x = 12x - 12y

Combining like terms:

12x - 12x = -12y

0 = -12y

Since the left side of the equation is 0, we can conclude that y = 0.

Therefore, the speed of the current is 0 km/h.

Now, we can substitute the value of y = 0 into Equation 1 to find the value of x:

12x = 10(x + 0)

12x = 10x

Subtracting 10x from both sides:

2x = 0

Dividing both sides by 2:

x = 0

Therefore, the speed of the boat in still water is 0 km/h.

Answer

The speed of the boat in still water is 0 km/h.