Question

Помогите за 50 баллов 2 задачи, С ОБЪЯСНЕНИЕМ Задача 1 От пристани на пирсе рыбхозяйства отправился в путь плот. Через 1 ч вдогонку отправилась моторная лодка, которая дошла до следующей пристани и сейчас же повернула обратно, вернулась к первой пристани. К моменту возвращения лодки плот уже проделал путь в 15 км. Найди скорость лодки по течению, если расстояние между пристанями составляет 24 км, а скорость течения реки на этом участке составляет 5 км/ч. Задача 2 От пристани на пирсе рыбхозяйства отправился в путь плот. Через 3 ч вдогонку отправилась моторная лодка, которая дошла до следующей пристани и сейчас же повернула обратно, вернулась к первой пристани. К моменту возвращения лодки плот уже проделал путь в 25 км. Найди скорость лодки по течению, если расстояние между пристанями составляет 24 км, а скорость течения реки на этом участке составляет 5 км/ч.

Answer 1

Ответ:

Пошаговое объяснение:

1.

x - скорость лодки, км/ч.

y - время, затраченное лодкой туда-обратно, ч.

1·5+5y=15 км проплыл плот к моменту возвращения лодки.

5y=15-5; y=10/5=2 ч - время, затраченное лодкой туда-обратно.

24/(x+5) +24/(x-5)=2                |2

12(x-5+x+5)=(x+5)(x-5)

24x=x²-25

x²-24x-25=0; D=576+100=676

x₁=(24-26)/2=-2/2=-1 - ответ не подходит по смыслу.

x₂=(24+26)/2=50/2=25 км/ч - скорость лодки.

25+5=30 км/ч - скорость лодки по течению.

Ответ: 30.

2.

x - скорость лодки, км/ч.

y - время, затраченное лодкой туда-обратно, ч.

3·5+5y=25 км проплыл плот к моменту возвращения лодки.

5y=25-15; y=10/5=2 ч - время, затраченное лодкой туда-обратно.

24/(x+5) +24/(x-5)=2 (решение смотри выше)

x=25 км/ч - скорость лодки.

25+5=30 км/ч - скорость лодки по течению.

Ответ: 30.

Answer 2

Problem 1: Speed of the Boat in Still Water

In this problem, we are given the following information: - The distance between the two piers is 24 km. - The speed of the river current is 5 km/h. - The raft has traveled a distance of 15 km by the time the motorboat returns to the first pier.

We need to find the speed of the motorboat in still water.

To solve this problem, we can use the concept of relative velocity. Let's assume the speed of the motorboat in still water is x km/h.

When the motorboat is traveling downstream (with the current), its effective speed is the sum of its speed in still water and the speed of the current. So, the effective speed of the motorboat downstream is (x + 5) km/h.

When the motorboat is traveling upstream (against the current), its effective speed is the difference between its speed in still water and the speed of the current. So, the effective speed of the motorboat upstream is (x - 5) km/h.

Now, let's calculate the time taken by the motorboat to travel from the first pier to the second pier and back.

Time taken downstream = Distance / Speed = 24 km / (x + 5) km/h

Time taken upstream = Distance / Speed = 24 km / (x - 5) km/h

Since the motorboat started 1 hour after the raft, the time taken by the motorboat to travel downstream and upstream should be 1 hour less than the time taken by the raft.

Time taken downstream by the motorboat = Time taken by the raft - 1 hour = 1 hour

Time taken upstream by the motorboat = Time taken by the raft - 1 hour = 1 hour

Now, we can set up the following equations:

24 km / (x + 5) km/h = 1 hour

24 km / (x - 5) km/h = 1 hour

Let's solve these equations to find the value of x.

Solving the first equation:

24 km / (x + 5) km/h = 1 hour

24 km = (x + 5) km/h

24 km * (x + 5) km/h = 1 hour * (x + 5) km/h

24(x + 5) = x + 5

24x + 120 = x + 5

24x - x = 5 - 120

23x = -115

x = -115 / 23

x = -5 km/h

Since the speed of the boat cannot be negative, we discard this solution.

Therefore, there is no valid solution for the speed of the motorboat in still water in this problem.

Problem 2: Speed of the Boat in Still Water

In this problem, we are given the following information: - The distance between the two piers is 24 km. - The speed of the river current is 5 km/h. - The raft has traveled a distance of 25 km by the time the motorboat returns to the first pier.

We need to find the speed of the motorboat in still water.

To solve this problem, we can use the same concept of relative velocity as in the previous problem. Let's assume the speed of the motorboat in still water is x km/h.

When the motorboat is traveling downstream (with the current), its effective speed is the sum of its speed in still water and the speed of the current. So, the effective speed of the motorboat downstream is (x + 5) km/h.

When the motorboat is traveling upstream (against the current), its effective speed is the difference between its speed in still water and the speed of the current. So, the effective speed of the motorboat upstream is (x - 5) km/h.

Now, let's calculate the time taken by the motorboat to travel from the first pier to the second pier and back.

Time taken downstream = Distance / Speed = 24 km / (x + 5) km/h

Time taken upstream = Distance / Speed = 24 km / (x - 5) km/h

Since the motorboat started 3 hours after the raft, the time taken by the motorboat to travel downstream and upstream should be 3 hours less than the time taken by the raft.

Time taken downstream by the motorboat = Time taken by the raft - 3 hours = 1 hour

Time taken upstream by the motorboat = Time taken by the raft - 3 hours = 1 hour

Now, we can set up the following equations:

24 km / (x + 5) km/h = 1 hour

24 km / (x - 5) km/h = 1 hour

Let's solve these equations to find the value of x.

Solving the first equation:

24 km / (x + 5) km/h = 1 hour

24 km = (x + 5) km/h

24 km * (x + 5) km/h = 1 hour * (x + 5) km/h

24(x + 5) = x + 5

24x + 120 = x + 5

24x - x = 5 - 120

23x = -115

x = -115 / 23

x = -5 km/h

Since the speed of the boat cannot be negative, we discard this solution.

Therefore, there is no valid solution for the speed of the motorboat in still water in this problem as well.

In both problems, the given information leads to an inconsistency, and there is no valid solution for the speed of the motorboat in still water.