Question

Вертолет пролетел 120 км по ветру и вернулся, на весь путь ушло 6 часов. Найдите скорость ветра, если скорость вертолета в ясный день 45 км/ч.

Answer 1

Ответ:

15 км/ч

Объяснение:

Расстояния S=120=S2
Всё время t=6
V вертолёта=45
V ветра=x
Составим уравнение по формулам t1+t2 = t = S/V+x + S2/V-x
120/45+x + 120/45-x=6
120(45-x)+120(45+x)=6(45-x)(45+x)
5400-120x+5400+120x=6(45²-x²
10800=6*2025-6x²
6x²=12150-10800
6x²=1350
x²=1350/6=225
x=√225=15 или -15
Скорость не может быть равна -15, значит x=15

Answer 2

Ответ:

15км/ч

Объяснение:

Пусть x - скорость ветра, то

120/(45+x)+120/(45-x)=6

120*45-120x+120*45+120x=6*45*45-6x²

6x²+240*45-6*45*45=0

x²=45*45-40*45

x²=5*45

x²=15²

x=±15 (отрицательная скорость ветра тут было бы против ветра, но в ней нет смысла, т.к. в условии по ветру.

Итого 15км/ч

Answer 3

Problem Analysis

We are given that a helicopter flew 120 km with the wind and returned, taking a total of 6 hours. We need to find the speed of the wind, given that the helicopter's speed on a clear day is 45 km/h.

Solution

Let's assume the speed of the wind is w km/h.

When the helicopter is flying with the wind, its effective speed will be the sum of its own speed and the speed of the wind: 45 + w km/h.

When the helicopter is flying against the wind, its effective speed will be the difference between its own speed and the speed of the wind: 45 - w km/h.

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

Calculation

Let's calculate the time taken for the helicopter to fly with the wind and against the wind.

The time taken to fly with the wind is given by:

120 km = (45 + w) km/h × t1

Simplifying the equation:

t1 = 120 km / (45 + w) km/h

The time taken to fly against the wind is given by:

120 km = (45 - w) km/h × t2

Simplifying the equation:

t2 = 120 km / (45 - w) km/h

We are also given that the total time taken for the entire journey is 6 hours:

t1 + t2 = 6 hours

Substituting the values of t1 and t2:

120 km / (45 + w) km/h + 120 km / (45 - w) km/h = 6 hours

Now we can solve this equation to find the value of w, the speed of the wind.

Solution

Let's solve the equation to find the speed of the wind.

120 km / (45 + w) km/h + 120 km / (45 - w) km/h = 6 hours

To simplify the equation, let's multiply both sides by (45 + w)(45 - w):

120 km(45 - w) + 120 km(45 + w) = 6 hours(45 + w)(45 - w)

Expanding and simplifying:

5400 km - 120w + 5400 km + 120w = 6(2025 - w^2)

Combining like terms:

10800 km = 12150 - 6w^2

Rearranging the equation:

6w^2 = 12150 - 10800

6w^2 = 1350

Dividing both sides by 6:

w^2 = 225

Taking the square root of both sides:

w = ±15

Since the speed of the wind cannot be negative, the speed of the wind is 15 km/h.

Answer

The speed of the wind is 15 km/h.