Question

2. Теплоход, собственная скорость которого 12 км/ч, прошел 42 км по течению реки и 27 км против течения, затратив на весь путь 6 часов. Какова скорость течения реки? в Пусть XH Z 78

Answer 1

Ответ:

Пусть х - скорость реки.

Мы знаем, что скорость лодки 12 км/ч.

Мы можем использовать формулу:

расстояние = скорость х время

Для расстояния вниз по течению:

42 = (12 + х) * (t1)

Для расстояния вверх по течению:

27 = (12 - х) * (t2)

Мы также знаем, что общее время составляет 6 часов:

т1 + т2 = 6

Мы можем заменить t1 и t2, используя первые два уравнения:

42 = (12 + х) * (6 - t2)

27 = (12 - х) * (t2)

Теперь мы можем решить систему уравнений, чтобы найти значение x (скорость реки)

Подставив t2 в первое уравнение:

42 = (12 + х) * (6 - (27/(12 - х)))

Тогда мы можем решить для х:

42 = (12 + х) * (6 - (27/(12 - х)))

х = 4 км/ч

Скорость реки 4 км/ч.

Answer 2

Problem Analysis

We are given the following information: - The speed of the boat in still water is 12 km/h. - The boat traveled 42 km downstream. - The boat traveled 27 km upstream. - The total time for the entire journey was 6 hours.

We need to find the speed of the river's current.

Solution

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

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. So, the effective speed downstream is (12 + x) km/h.

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. So, the effective speed upstream is (12 - x) km/h.

We can use the formula distance = speed × time to calculate the time taken for each leg of the journey.

The time taken to travel downstream is 42 / (12 + x) hours.

The time taken to travel upstream is 27 / (12 - x) hours.

According to the problem, the total time for the entire journey is 6 hours. So, we can write the equation:

(42 / (12 + x)) + (27 / (12 - x)) = 6

To solve this equation, we can multiply through by the denominators to eliminate the fractions:

42(12 - x) + 27(12 + x) = 6(12 + x)(12 - x)

Simplifying the equation:

504 - 42x + 324 + 27x = 6(144 - x^2)

828 - 15x = 864 - 6x^2

Rearranging the equation:

6x^2 - 15x - 36 = 0

Now we can solve this quadratic equation to find the value of x.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 6, b = -15, and c = -36.

Plugging in the values:

x = (-(-15) ± √((-15)^2 - 4(6)(-36))) / (2(6))

Simplifying:

x = (15 ± √(225 + 864)) / 12

x = (15 ± √1089) / 12

x = (15 ± 33) / 12

We have two possible solutions for x:

1. x = (15 + 33) / 12 = 48 / 12 = 4 2. x = (15 - 33) / 12 = -18 / 12 = -1.5

Since the speed of the current cannot be negative, we can conclude that the speed of the river's current is 4 km/h.

Answer

The speed of the river's current is 4 km/h.