Question

The speed of a plane in still air is x miles per hour. The wind blows at a constant speed of y miles per hour in an unvarying direction. Flying into a headwind (against the wind), the plane takes 4 hours to travel 500 miles. Flying with a tailwind (with the wind), the plane takes 3 hours to travel 465 miles. Write a system of linear equations to represent the scenario.(1 point)
Responses

{4(x−y)=5003(x+y)=465
enlarged left brace start layout first row 4 left parenthesis x minus y right parenthesis equals 500 second row 3 left parenthesis x plus y right parenthesis equals 465 end layout

{4x−y=5003x+y=465
enlarged left brace start layout first row 4 x minus y equals 500 second row 3 x plus y equals 465 end layout

{4(x+y)=5003(x−y)=465
enlarged left brace start layout first row 4 left parenthesis x plus y right parenthesis equals 500 second row 3 left parenthesis x minus y right parenthesis equals 465 end layout

{4x+y=5003x−y=465
enlarged left brace start layout first row 4 x plus y equals 500 second row 3 x minus y equals 465 end layout
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Answer 1

To represent the scenario with a system of linear equations, we need to analyze the given information:

1. **Flying into a headwind (against the wind)**:
- The effective speed of the plane is \( (x - y) \) miles per hour.
- The time taken to travel 500 miles is given as 4 hours.
- Therefore, we can form the equation:
\[
4(x - y) = 500
\]

2. **Flying with a tailwind (with the wind)**:
- The effective speed of the plane is \( (x + y) \) miles per hour.
- The time taken to travel 465 miles is given as 3 hours.
- Therefore, we can form the equation:
\[
3(x + y) = 465
\]

Now we can write the system of linear equations based on these two scenarios:

\[
\begin{cases}
4(x - y) = 500 \\
3(x + y) = 465
\end{cases}
\]

From the options given, this corresponds to:

**Option:**
\(\{4(x - y) = 500, 3(x + y) = 465\}\)

So, the correct response is:

**{4(x−y)=500, 3(x+y)=465}**