Question

За 4ч катер проходит по течению реки растояние, в 2.4 раза больше , чем за 2ч против течения . какова скорость катера в стоячей воде , если скорость течения 1.5 км/ч ? уровнением если можно )

Answer 1

Пусть x расстояние, кот. проходит катер против течения.

Тогда 2,4 x расстояние, кот. проходит катер по течению.

Скорость против течения тогда x/2, а по течению x/2,4.

Зная, что скорость течения 1,5 км/ч, составим уравнение, при этом удвоим скорость течения, чтобы можно было уровнять обе скорости.

Получим: x/2+3=2.4x/4

(x+6)/2=2.4/4  Теперь умножим обе части на 4, получим:

2(x+6)=2.4x

x=30 Это расстояние,кот.прошел катер против течения; 2,4*30=72 км-по течению

72/4=18 км/ч скорость по течению, 30/2=15 км/ч скорость против течения

А теперь ответим на главный вопрос: 15+1,5=16,5 км/ч собственная скорость катера.

Answer 2

Problem Analysis

We are given that a boat travels a distance in 4 hours downstream (with the current) that is 2.4 times greater than the distance it travels in 2 hours upstream (against the current). We need to find the speed of the boat in still water, given that the speed of the current is 1.5 km/h.

Solution

Let's assume the speed of the boat in still water is x km/h.

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current. Therefore, the distance traveled downstream in 4 hours is given by 4(x + 1.5).

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the distance traveled upstream in 2 hours is given by 2(x - 1.5).

According to the problem statement, the distance traveled downstream is 2.4 times greater than the distance traveled upstream. Therefore, we can write the equation:

4(x + 1.5) = 2.4 * 2(x - 1.5)

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

Calculation

Expanding the equation:

4x + 6 = 4.8x - 7.2

Rearranging the terms:

4.8x - 4x = 6 + 7.2

0.8x = 13.2

Dividing both sides by 0.8:

x = 13.2 / 0.8

x = 16.5

Answer

The speed of the boat in still water is 16.5 km/h.

Verification

To verify our answer, let's substitute the value of x back into the equation and check if both sides are equal.

Left-hand side of the equation:

4(x + 1.5) = 4(16.5 + 1.5) = 4(18) = 72

Right-hand side of the equation:

2.4 * 2(x - 1.5) = 2.4 * 2(16.5 - 1.5) = 2.4 * 2(15) = 2.4 * 30 = 72

Both sides of the equation are equal, which confirms that our answer is correct.

Therefore, the speed of the boat in still water is 16.5 km/h.