Question

катер проплывает 8 км против течения и еще 30 км по течению за то же время, за которое плот может проплыть по этой реке 4 км. Скорость катера в стоячей воде равна 18 км/ч. Найдите скорость течения реки. P.S. ОООООоочень нужно

Answer 1

Пусть х км/ч -скорость течения реки;
(18-х )км/ч -скорость катера против течения;
(18+х)км/ч скорость катера по течению;
Решение:

8/(18-х )+30/(18+х) = 4/х ;
144х +8х² +540х -30х² = 1296 -4х² тогда,
18х² -684х +1296 =0 или х² -38х+72 =0 ;
х1= 36 и х2 =2
Ответ: 2 км/ч (скорость течения реки).

Answer 2

Problem Analysis

We are given the following information: - A boat travels 8 km against the current and then 30 km with the current in the same amount of time. - The boat's speed in still water is 18 km/h. - We need to find the speed of the river's current.

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

Solution

To solve this problem, we can use the formula: speed = distance / time.

Let's calculate the time it takes for the boat to travel 8 km against the current and 30 km with the current.

The time taken to travel 8 km against the current is: 8 / (18 - x).

The time taken to travel 30 km with the current is: 30 / (18 + x).

Since both times are the same, we can set up the following equation:

8 / (18 - x) = 30 / (18 + x).

Now, let's solve this equation to find the value of x.

Calculation

To solve the equation 8 / (18 - x) = 30 / (18 + x), we can cross-multiply:

8 * (18 + x) = 30 * (18 - x).

Simplifying the equation:

144 + 8x = 540 - 30x.

Combining like terms:

38x = 396.

Dividing both sides by 38:

x = 10.42.

Therefore, the speed of the river's current is approximately 10.42 km/h.

Answer

The speed of the river's current is approximately 10.42 km/h.