Question

Прогулочный теплоход отправился вниз по течению реки от пристани А и причалил к пристани В. После 0,8 часа стоянки теплоход отправился обратно и через 12 часов после отплытия из А вернулся на эту же пристань. Какова скорость теплохода в стоячей воде, если расстояние между пристанями А и В равно 42 км, а скорость течения реки 2 км/ч?​

Answer 1

Объяснение:

Пусть скорость теплохода в стоячей воде равна х км/ч.      ⇒

$\frac{42}{x+2}+\frac{42}{x-2}+0,8=12\\ \frac{42}{x+2}+\frac{42}{x-2}=12-0,8=\\ \frac{42}{x+2}+\frac{42}{x-2}=11,2\\42*(x-2)+ 42*(x+2)=11,2*(x+2)*(x-2)\ |*\frac{5}{14} \\15*(x-2)+15*(x+2)=4*(x^2-4)\\15x-30+15x+30=4x^2-16\\30x=4x^2-16\ |:2\\2x^2-15x-8=0\\D=289\ \ \ \ \sqrt{D}=17\\ x_1=-0,5\notin\ \ \ \ x_2=8\in.$

Ответ: скорость теплохода в стоячей воде равна 8 км/ч.

Answer 2

Problem Analysis

We are given the following information: - A pleasure boat travels downstream from port A to port B. - After a 0.8-hour stop at port B, the boat returns upstream and arrives back at port A after 12 hours. - The distance between ports A and B is 42 km. - The speed of the river current is 2 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.

When the boat is traveling downstream from port A to port B, it benefits from the speed of the river current. Therefore, the effective speed of the boat is the sum of its speed in still water and the speed of the river current. So, the effective speed downstream is (x + 2) km/h.

The time taken to travel downstream from port A to port B can be calculated using the formula:

Time = Distance / Speed

Substituting the values, we have:

Time downstream = 42 / (x + 2)

After a 0.8-hour stop at port B, the boat starts traveling upstream from port B to port A. In this case, the boat has to overcome the speed of the river current. Therefore, the effective speed of the boat upstream is the difference between its speed in still water and the speed of the river current. So, the effective speed upstream is (x - 2) km/h.

The time taken to travel upstream from port B to port A can be calculated using the same formula:

Time = Distance / Speed

Substituting the values, we have:

Time upstream = 42 / (x - 2)

According to the problem, the total time taken for the round trip is 12 hours. Therefore, the sum of the time taken downstream and the time taken upstream should be equal to 12 hours:

Time downstream + Time upstream = 12

Substituting the values, we have:

42 / (x + 2) + 42 / (x - 2) = 12

To solve this equation, we can multiply both sides by (x + 2)(x - 2) to eliminate the denominators:

42(x - 2) + 42(x + 2) = 12(x + 2)(x - 2)

Simplifying the equation:

42x - 84 + 42x + 84 = 12(x^2 - 4)

84x = 12x^2 - 48

12x^2 - 84x - 48 = 0

Dividing both sides by 12:

x^2 - 7x - 4 = 0

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

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values:

x = (-(-7) ± √((-7)^2 - 4(1)(-4))) / (2(1))

Simplifying:

x = (7 ± √(49 + 16)) / 2

x = (7 ± √65) / 2

Therefore, the speed of the boat in still water can be either:

x = (7 + √65) / 2 or x = (7 - √65) / 2

Let's calculate the values:

x = (7 + √65) / 2 ≈ 7.82 km/h

x = (7 - √65) / 2 ≈ -0.82 km/h

Since the speed of the boat cannot be negative, we can conclude that the speed of the boat in still water is approximately 7.82 km/h.

Answer

The speed of the pleasure boat in still water is approximately 7.82 km/h.