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?

To solve the problem, we need to account for the effect of the headwind on the airplane's speed.

### Given:
- Airplane's speed in still air: 500 mph
- Headwind: 50 mph
- Distance to travel: 900 miles

When the airplane is flying into the wind, the effective speed is reduced by the speed of the headwind.

### Effective speed of the airplane:
\[
\text{Effective speed} = 500 \, \text{mph} - 50 \, \text{mph} = 450 \, \text{mph}
\]

Now, to calculate the time it takes to travel 900 miles at 450 mph, we use the formula for time:

\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{900 \, \text{miles}}{450 \, \text{mph}} = 2 \, \text{hours}
\]

### Conclusion:
It will take the airplane **2 hours** to travel 900 miles into the wind.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:
1. How long would the trip take if there was no wind?
2. What would happen if the airplane encountered a tailwind instead?
3. How do different wind speeds affect flight times?
4. What formula relates distance, speed, and time in such problems?
5. How does wind resistance impact fuel efficiency in flights?

**Tip:** When calculating travel times with wind, always adjust the airplane’s speed by adding or subtracting the wind speed depending on whether it’s a tailwind or headwind.

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

Learn how to calculate the time it takes for an airplane traveling at 500 mph in still air to cover 900 miles with a 50-mph headwind. This problem involves the speed-time-distance relationship and uses basic algebraic concepts. Ideal for students in Grades 6-8.

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