Question

Решить задачу , составить уравнение, вертолет пролетел расстояние между двумя городами при попутном ветре за 6 часов 20 минут , а при встречном ветре за 7 часов , Определить расстояние между городами и собственную скорость вертолета , если скорость ветра была равна 9 км\ч

Answer 1

Х км/ч собственная скорость вертолета,
х+9 км/ч скорость вертолета при попутном ветре,
х-9 км/ч скорость вертолета при встречном ветре.
6ч20мин=6 1/3ч
6 1/3*(х+9)=7(х-9)
6 1/3х + 6 1/3 * 9= 7х-63
19/3х + 19/3 * 9= 7х-63
19/3х + 19*3= 7х-63
7х-19/3х=57+63
2/3х=120
х=120:2/3
х=120*3/2
х=60*3
х=180 км/ч собственная скорость вертолета
180+9=189 км/ч скорость вертолета при попутном ветре
189*6 1/3=189*19/3= 63*19=1197 км расстояние между городами

Ответ: 1197км; 180км/ч

Answer 2

Problem Analysis

To solve this problem, we need to determine the distance between two cities and the helicopter's own speed. We are given the time it takes for the helicopter to travel between the cities in two scenarios: with a tailwind and against a headwind. Additionally, we are given the speed of the wind.

Let's denote the distance between the cities as d and the speed of the helicopter as v. The speed of the wind is given as 9 km/h.

Solution

To find the distance between the cities, we can use the formula:

Distance = Speed × Time

Let's calculate the distance when the helicopter is flying with the tailwind and against the headwind.

When flying with the tailwind, the effective speed of the helicopter is the sum of its own speed and the speed of the wind. The time taken is 6 hours and 20 minutes, which is equivalent to 6.33 hours.

Distance with tailwind = (v + 9) × 6.33

When flying against the headwind, the effective speed of the helicopter is the difference between its own speed and the speed of the wind. The time taken is 7 hours.

Distance against headwind = (v - 9) × 7

Since the distance between the cities is the same in both scenarios, we can set up the following equation:

(v + 9) × 6.33 = (v - 9) × 7

Now, let's solve this equation to find the value of v.

Calculation

Expanding the equation:

6.33v + 56.97 = 7v - 63

Rearranging the terms:

6.33v - 7v = -63 - 56.97

Simplifying:

-0.67v = -119.97

Dividing both sides by -0.67:

v = 178.76

The speed of the helicopter is approximately 178.76 km/h.

Now, let's substitute this value of v into one of the distance equations to find the distance between the cities.

Using the equation for flying with the tailwind:

Distance with tailwind = (178.76 + 9) × 6.33 = 1191.47 km

Therefore, the distance between the cities is approximately 1191.47 km.

Answer

The distance between the two cities is approximately 1191.47 km and the speed of the helicopter is approximately 178.76 km/h.