Question

Теп­ло­ход про­хо­дит по те­че­нию реки до пунк­та на­зна­че­ния 285 км и после сто­ян­ки воз­вра­ща­ет­ся в пункт от­прав­ле­ния. Найдите скорость течения, если скорость теплохода в неподвижной воде равна 34 км/ч, стоянка длится 19 часов, а в пункт отправления теплоход возвращается через 36 часов после отплытия из него.

Answer 1

Основные формулы для решения задачи:
V по теч. = Vc + V теч. - скорость по течению реки
V против теч. = Vc - V теч. - скорость против течения
t по теч.= S/V по теч. - время на путь по течению реки
t против теч. = S/V против теч. - время на путь против течения реки
По условию:
Скорость теплохода в неподвижной воде -это собственная скорость теплохода (Vc) .
Путь в одну сторону S = 285 км
Время на путь туда-обратно t = 36 - 19 = 17 часов.
Пусть скорость течения Vc = х км/ч
Путь по течению:
Скорость Vпо теч. = (34 + х ) км/ч
Время в пути t₁= 285/(34+x) ч.
Путь против течения:
Скорость V против теч. = (34 - х) км/ч
Время в пути t₂ = 285/(34-x) ч.
Время на путь туда-обратно : t₁ +t₂ = 17 ч.
Уравнение.
285/(34+х) + 285/(34-х) = 17 |×(34+x)(34-x)
знаменатели ≠ 0 ⇒ х≠ 34 ; х≠ = -34
285(34-x) + 285(34+x) = 17(34+x)(34-x)
9690 - 285x + 9690 + 285x= 17(34² - x² )
19380 = 17(1156 -x²) |÷17
1140= 1156 - x²
x²= 1156-1140
x² = 16
x₁ = - 4 не удовлетворяет условию задачи
х₂ = 4 (км/ч) Vтеч.
Ответ: 4 км/ч скорость течения реки.

Answer 2

Problem Analysis

We are given the following information: - The distance from the starting point to the destination is 285 km. - The speed of the boat in still water is 34 km/h. - The boat stays at the destination for 19 hours. - The boat returns to the starting point 36 hours after departing from it.

We need to find the speed of the river current.

Solution

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

When the boat is traveling from the starting point to the destination, it is moving against the current. Therefore, the effective speed of the boat is the difference between the speed of the boat in still water and the speed of the current: 34 - x km/h.

When the boat is returning from the destination to the starting point, it is moving with the current. Therefore, the effective speed of the boat is the sum of the speed of the boat in still water and the speed of the current: 34 + x km/h.

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

Let's calculate the time taken for the boat to travel from the starting point to the destination:

time1 = distance / speed1

where: - distance = 285 km - speed1 = 34 - x km/h

Similarly, let's calculate the time taken for the boat to return from the destination to the starting point:

time2 = distance / speed2

where: - distance = 285 km - speed2 = 34 + x km/h

We know that the boat stays at the destination for 19 hours and returns to the starting point 36 hours after departing from it. Therefore, the total time for the round trip is:

total time = time1 + 19 + time2 + 36

We can substitute the values of time1 and time2 into the equation above and solve for x.

Let's calculate the value of x using the given information.

Calculation

Using the formula speed = distance / time, we can calculate the time taken for each leg of the journey:

time1 = 285 / (34 - x)

time2 = 285 / (34 + x)

The total time for the round trip is:

total time = time1 + 19 + time2 + 36

Substituting the values of time1 and time2:

total time = (285 / (34 - x)) + 19 + (285 / (34 + x)) + 36

Simplifying the equation:

total time = (285(34 + x) + 19(34 - x) + 36(34 - x)(34 + x)) / (34^2 - x^2)

Multiplying and simplifying further:

total time = (9690 + 285x + 646 - 19x + 1224(1156 - x^2)) / (1156 - x^2)

Simplifying the equation:

total time = (11520 + 266x + 1224(1156 - x^2)) / (1156 - x^2)

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

Answer

To find the speed of the river current, we need to solve the equation:

total time = (11520 + 266x + 1224(1156 - x^2)) / (1156 - x^2)

Unfortunately, the equation is quite complex and cannot be easily solved algebraically. It requires numerical methods or approximation techniques to find the value of x.

Please note that the given information does not provide enough data to calculate the speed of the river current accurately. Additional information or assumptions are needed to solve the problem.

If you have any further questions, please let me know!