An airplane that travels 

500500 

mph in still air encounters a 

5050​-mph 

headwind. How long will it take the plane to travel 

900900 

mi into the​ wind?

To solve the problem, we need to determine how long it will take the airplane to travel 900,900 miles into the wind, given the airplane's speed and the wind speed.

### Given:
- The airplane's speed in still air: 500,500 mph.
- The headwind speed: 50 mph.
- The distance to travel: 900,900 miles.

### Step-by-Step Solution:

1. **Determine the effective speed of the airplane**:  
   Since the airplane is encountering a headwind, the effective speed of the airplane will be reduced by the wind speed.  
   
   \[
   \text{Effective speed} = \text{Airplane speed} - \text{Wind speed}
   \]
   
   \[
   \text{Effective speed} = 500,500 - 50 = 500,450 \, \text{mph}
   \]

2. **Calculate the time to travel**:  
   Time is calculated using the formula:

   \[
   \text{Time} = \frac{\text{Distance}}{\text{Speed}}
   \]
   
   Substituting the values:

   \[
   \text{Time} = \frac{900,900}{500,450} \, \text{hours}
   \]

Let me calculate this for you.The airplane will take approximately **1.8 hours** to travel 900,900 miles into the wind.

Would you like more details, or do you have any other questions?

Here are 5 related questions for further exploration:
1. How would the time change if the headwind speed increased to 100 mph?
2. What if the airplane had a tailwind instead of a headwind? How would this affect the travel time?
3. How far would the plane travel in 5 hours with the same headwind?
4. How long would it take the airplane to travel 900,900 miles with no wind?
5. What would happen if the plane's speed in still air were increased by 10%?

**Tip:** When solving word problems, clearly separate the given information, the unknowns, and the formulas you plan to use. This helps avoid confusion and ensures accurate calculations.

An airplane that travels 500 mph in still air encounters a 50-mph headwind. How long will it take the plane to travel 900 mi into the wind?

Learn how to calculate the time for an airplane to travel 900 miles with a 50-mph headwind, reducing its speed from 500 mph. This problem uses key algebraic concepts, including the relationship between speed, distance, and time, and is ideal for students in Grades 6-8.

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