An airplane leaves Los Angeles and travels 5 hours to New York City. The return trip travels along the same route and takes 6 hours and 15 minutes because the plane travels 99 miles per hour slower due to a headwind. Find the distance that the plane flies between the two cities.

The distance that the plane flies between the two cities is what amount of miles.

To find the distance between Los Angeles and New York City, we can use the relationship between distance, speed, and time. The formula to use is:

\[
\text{Distance} = \text{Speed} \times \text{Time}
\]

### Step 1: Define the variables.
- Let \( d \) be the distance between the two cities.
- Let \( v \) be the speed of the plane on the trip from Los Angeles to New York City.
- The time taken to travel from Los Angeles to New York City is 5 hours.
- The speed on the return trip (from New York City to Los Angeles) is \( v - 99 \) miles per hour due to the headwind.
- The time taken for the return trip is 6 hours and 15 minutes, which is equivalent to \( 6.25 \) hours (since 15 minutes is 0.25 hours).

### Step 2: Set up the equations.
For the trip from Los Angeles to New York City:
\[
d = v \times 5
\]

For the return trip from New York City to Los Angeles:
\[
d = (v - 99) \times 6.25
\]

### Step 3: Equate the two expressions for distance.
Since both equations represent the same distance \( d \), we can set them equal:
\[
v \times 5 = (v - 99) \times 6.25
\]

### Step 4: Solve for \( v \).
Expand and simplify the equation:
\[
5v = 6.25v - 618.75
\]
Subtract \( 5v \) from both sides:
\[
0 = 1.25v - 618.75
\]
Add 618.75 to both sides:
\[
1.25v = 618.75
\]
Finally, solve for \( v \) by dividing both sides by 1.25:
\[
v = \frac{618.75}{1.25} = 495 \text{ miles per hour}
\]

### Step 5: Calculate the distance \( d \).
Now that we have \( v = 495 \) miles per hour, we can find the distance using the first equation \( d = v \times 5 \):
\[
d = 495 \times 5 = 2475 \text{ miles}
\]

### Conclusion:
The distance that the plane flies between Los Angeles and New York City is **2475 miles**.

Would you like more details or have any questions?

### Related Questions:
1. How do you convert minutes to a decimal of an hour?
2. What other factors could affect the time it takes for a plane to travel between two cities?
3. How do you solve equations with variables on both sides?
4. What is the effect of wind on airplane speed?
5. How can you check the accuracy of your solution in word problems?

### Tip:
When solving word problems involving time, speed, and distance, always convert all time units to the same format (e.g., hours) to avoid errors in calculation.

Learn how to calculate the distance traveled by an airplane between Los Angeles and New York City, considering different speeds due to headwind. This problem involves using the distance, speed, and time formula. Suitable for Grades 7-9.

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