Question

Лодка шла против течения реки 4,5 часа и по течению 2,1 час.Найти скорость лодки в стоячей воде,если она прошла всего 52,2 км течения реки ровна 3 км/ч?

Answer 1

Смотри. У тебя дано расстояние равное 52,2.
Дано время движения против течения и по течению. 4,5 и 2,1 часа соответственно.
Скорость течения реки тоже известна, 3 км.ч.
Следовательно скорость катера по течению будет равна x+3км.ч.
А против течения x-3км.ч.
Где икс - собственная скорость катера.
Составляем уравнение.
52,2=(x+3)*2,1=(x-3)*4,5.
Получаем.
(x+3)*2,1-(x-3)*4,5=0.
2,1x+6,3-4,5x+13,5=0.
Числа в одну сторону, иксы в другую.
2.1x-4,5x=-6,3-13,5
-2,4x=-19.8
x=8,25 км.ч(когда делишь отрицательное число на отрицательное, получаешь положительное)
Ответ: Скорость катера равна 8,25 км.ч

Answer 2

Problem Analysis

We are given the following information: - The boat traveled against the current of the river for 4.5 hours. - The boat traveled with the current of the river for 2.1 hours. - The total distance traveled by the boat is 52.2 km. - The speed of the current is 3 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 against the current, its effective speed is reduced by the speed of the current. So, the speed of the boat against the current is (x - 3) km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So, the speed of the boat with the current is (x + 3) km/h.

We can use the formula distance = speed × time to calculate the distances traveled in each case.

The distance traveled against the current is (x - 3) × 4.5 km.

The distance traveled with the current is (x + 3) × 2.1 km.

According to the problem, the total distance traveled is 52.2 km. So, we can write the equation:

(x - 3) × 4.5 + (x + 3) × 2.1 = 52.2

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

Calculation

Expanding the equation, we get:

4.5x - 13.5 + 2.1x + 6.3 = 52.2

Combining like terms, we have:

6.6x - 7.2 = 52.2

Adding 7.2 to both sides, we get:

6.6x = 59.4

Dividing both sides by 6.6, we get:

x = 9

Answer

The speed of the boat in still water is 9 km/h.