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The problem involves an airplane traveling a distance of 360 miles with the wind and against the wind, and we need to calculate the speed of the airplane in still air and the speed of the wind.

Let's define the variables:

- Let \( x \) be the speed of the airplane in still air (in miles per hour).
- Let \( y \) be the speed of the wind (in miles per hour).
  
The plane takes:
- 2 hours to travel 360 miles with the wind: the effective speed is \( x + y \).
- 3 hours to travel 360 miles against the wind: the effective speed is \( x - y \).

We can now form two equations based on the time, speed, and distance formula \( \text{distance} = \text{speed} \times \text{time} \):

1. \( 360 = (x + y) \times 2 \) or \( x + y = 180 \)
2. \( 360 = (x - y) \times 3 \) or \( x - y = 120 \)

Now, we can solve these two equations to find \( x \) and \( y \).

**Step 1:** Add the two equations:
\[
(x + y) + (x - y) = 180 + 120
\]
\[
2x = 300
\]
\[
x = 150
\]

**Step 2:** Substitute \( x = 150 \) into the first equation:
\[
x + y = 180
\]
\[
150 + y = 180
\]
\[
y = 30
\]

Thus, the speed of the airplane in still air is **150 miles per hour**, and the wind speed is **30 miles per hour**.

Would you like any further clarification on the solution?

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Here are 5 related questions to further your understanding:

1. How would the airplane's travel time change if the wind speed increased by 10 mph?
2. What would happen to the effective speed if the wind direction changed to perpendicular to the airplane's path?
3. How can you use this method to calculate the time for other distances?
4. What is the general form of equations to solve similar problems for any distance and time?
5. How do factors like drag and altitude affect the speed of an airplane in real-world scenarios?

**Tip:** In problems with two unknowns, always look to create two independent equations for solving them simultaneously.

An airplane flying with the wind takes 2 hours to travel a distance of 360 miles. The return trip takes 3 hours flying against the wind. What is the speed of the airplane in still air and how fast is the wind blowing?

Solve an algebraic problem involving an airplane flying with and against the wind. Learn how to calculate the speed of the airplane in still air and the wind speed using systems of equations and the formula for distance, speed, and time. Suitable for Grades 8-10.

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