Question

Краткая запись задачи ( скорость , время , расстояние , ): с аэродрома вылетел вертолет со скоростью 210 км\ч. Через 2 часа с этого же аэродрома вылетел вслед за вертолетом самолет, который через 3 часа после своего вылета перегнал вертолет на 840 км. Найди скорость самолета.

Answer 1

1) 210÷2+840÷3=295все все

Answer 2

Обозначения: S1-расстояние, которое пролетел вертолет; S2- расстояние, которое пролетел самолет; V1- скорость вертолета; V2- скоротость самолета; t1- время полета вертолета; t2- время полета самолета. Имеющиеся данные: V1=210 (км/ч) t1=5 (ч) t2=3(ч) Требуется найти: V2 Решение: S=V*t S1=V1*t1=210*5=1050(км) S2=V2*t2=3*V2 S2=S1+840 3*V2=1050+840 V2=630(км/ч) Ответ: V2=630(км/ч)

Answer 3

Problem Statement:

A helicopter took off from an aerodrome with a speed of 210 km/h. Two hours later, an airplane took off from the same aerodrome and chased the helicopter. After 3 hours of its takeoff, the airplane overtook the helicopter at a distance of 840 km. Find the speed of the airplane.

Solution:

Let's denote the speed of the airplane as x km/h.

To solve this problem, we can use the formula:

Distance = Speed × Time

For the helicopter: - Speed = 210 km/h - Time = t hours (since it took off 2 hours before the airplane)

For the airplane: - Speed = x km/h - Time = t - 3 hours (since it overtook the helicopter after 3 hours of its takeoff)

We know that the distance covered by both the helicopter and the airplane is the same, which is 840 km.

Using the formula, we can set up the following equation:

210t = x(t - 3)

Simplifying the equation, we get:

210t = xt - 3x

Rearranging the equation, we get:

xt - 210t = 3x

Factoring out x, we get:

t(x - 210) = 3x

Dividing both sides of the equation by (x - 210), we get:

t = (3x) / (x - 210)

Now, we can substitute the value of t into the equation to solve for x:

840 = x(t - 3)

Substituting t = (3x) / (x - 210), we get:

840 = x(((3x) / (x - 210)) - 3)

Simplifying the equation, we get:

840 = x(3 - (630 / (x - 210)))

Multiplying both sides of the equation by (x - 210), we get:

840(x - 210) = x(3(x - 210) - 630)

Expanding and simplifying the equation, we get:

840x - 176,400 = 3x^2 - 630x - 1,890

Rearranging the equation, we get:

3x^2 - 1,470x - 174,510 = 0

Now, we can solve this quadratic equation to find the value of x using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = 3, b = -1,470, and c = -174,510.

Substituting these values into the quadratic formula, we get:

x = (-(-1,470) ± √((-1,470)^2 - 4(3)(-174,510))) / (2(3))

Simplifying the equation, we get:

x = (1,470 ± √(2,160,900 + 2,087,640)) / 6

x = (1,470 ± √(4,248,540)) / 6

x = (1,470 ± 2,061.68) / 6

Now, we can calculate the two possible values of x:

x₁ = (1,470 + 2,061.68) / 6 ≈ 551.95

x₂ = (1,470 - 2,061.68) / 6 ≈ -181.95

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

Therefore, the speed of the airplane is approximately 551.95 km/h.

Answer:

The speed of the airplane is approximately 551.95 km/h.