Question

Помогите пожалуйста!! Катер отправился в путь в 10 часов утра, прошел 8 км против течения реки и сделал остановку на 1 час. После этого он прошел ещё 30 км по течению и прибыл в пункт назначения в 13 часов. Найдите собственную скорость катера, если скорость течения реки 2 км/ч.

Answer 1

Ответ:

1)с 10.00 до 13.00 - 3 часа
3-1=2 часа - время в пути всего
2)
Пусть собственная скорость катера - х км/ч .
Время в пути против течения реки - 8/(х-2) ч.
Время в пути по течению реки - 30/(х+2) ч.
Уравнение:
8/(х-2) + 30/(х+2) = 2
8(х+2) +30(х-2)= 2(х-2)(х+2)
8х+16+30х-60= 2х²-8
38х-44=2х²-8
2х²-8-38х+44=0
2х² -38х+36=0 :2
х²-19х+18=0
D= 361-4*18*1= 361-72=289
x₁= (19+17)/2 = 18 - собственная скорость катера (Vc)
x₂= (19-17)/2 =1 - не удовлетворяет условию задачи, т.к. собственная скорость катера не может быть меньше скорости течения реки.

Ответ : V c = 18 км/ч

Объяснение:

Answer 2

Ответ:

x - скорость катера

x-2 - скорость против течения

x+2 - скорость по течению

8 км против течения прошел за 8/x-2 часов

30 км по течению прошел за30/x+2  часов

Answer 3

Calculation of the Boat's Speed

To find the speed of the boat, we need to calculate the time it took for the boat to travel from the starting point to the destination.

Given information: - Departure time: 10:00 AM - Distance traveled against the current: 8 km - Stoppage time: 1 hour - Distance traveled with the current: 30 km - Arrival time: 1:00 PM - Speed of the river current: 2 km/h

Let's break down the journey into two parts: the distance traveled against the current and the distance traveled with the current.

1. Distance traveled against the current: - The boat traveled 8 km against the current. - Since the speed of the current is 2 km/h, the effective speed of the boat against the current is the boat's speed minus the current's speed. - Let's assume the speed of the boat against the current is B km/h. - The time taken to travel 8 km against the current can be calculated using the formula: time = distance / speed. - So, the time taken to travel 8 km against the current is 8 / (B - 2) hours.

2. Distance traveled with the current: - The boat traveled 30 km with the current. - Since the speed of the current is 2 km/h, the effective speed of the boat with the current is the boat's speed plus the current's speed. - Let's assume the speed of the boat with the current is B km/h. - The time taken to travel 30 km with the current can be calculated using the formula: time = distance / speed. - So, the time taken to travel 30 km with the current is 30 / (B + 2) hours.

Now, let's calculate the total time taken for the journey:

- Departure time: 10:00 AM - Stoppage time: 1 hour - Arrival time: 1:00 PM

The total time taken for the journey is the sum of the time taken to travel against the current, the stoppage time, and the time taken to travel with the current.

Total time = (8 / (B - 2)) + 1 + (30 / (B + 2))

Since the arrival time is 1:00 PM, the total time taken for the journey is 3 hours.

Now, we can solve the equation:

(8 / (B - 2)) + 1 + (30 / (B + 2)) = 3

Simplifying the equation, we get:

8 / (B - 2) + 30 / (B + 2) = 2

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

8(B + 2) + 30(B - 2) = 2(B - 2)(B + 2)

Simplifying further:

8B + 16 + 30B - 60 = 2(B^2 - 4)

Combining like terms:

38B - 44 = 2B^2 - 8

Rearranging the equation:

2B^2 - 38B + 8 = 44

2B^2 - 38B - 36 = 0

Now, we can solve this quadratic equation to find the value of B, which represents the speed of the boat.

Using the quadratic formula: B = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = -38, and c = -36.

Plugging in the values:

B = (-(-38) ± √((-38)^2 - 4 * 2 * -36)) / (2 * 2)

Simplifying:

B = (38 ± √(1444 + 288)) / 4

B = (38 ± √1732) / 4

B = (38 ± 41.62) / 4

B ≈ 19.81 or B ≈ -0.81

Since the speed of the boat cannot be negative, we can discard the negative value.

Therefore, the speed of the boat is approximately 19.81 km/h.

Please note that this calculation assumes a constant speed throughout the journey and does not take into account other factors such as wind or variations in the current.