To solve the given problem, we need to set up the equation correctly based on the airplane's speed and the influence of the wind on its travel time.
Let [tex]\( x \)[/tex] be the speed of the airplane in still air, in miles per hour (mph).
### Step-by-Step Solution:
1. Determine the speed of the airplane with and against the wind:
- With the wind: [tex]\( x + 20 \)[/tex] mph
- Against the wind: [tex]\( x - 20 \)[/tex] mph
2. Determine the time taken for each leg of the trip:
- The distance for each leg is 350 miles.
- Time taken to travel with the wind: [tex]\( \frac{350}{x + 20} \)[/tex] hours
- Time taken to travel against the wind: [tex]\( \frac{350}{x - 20} \)[/tex] hours
3. Set up the equation for the total round-trip time:
- The total time for the round trip is given as 6 hours.
- Therefore, we write the equation:
[tex]\[
\frac{350}{x + 20} + \frac{350}{x - 20} = 6
\][/tex]
### Final Equation:
To rewrite it by replacing [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
[tex]\[
a = \frac{350}{x + 20}, \quad b = \frac{350}{x - 20}, \quad c = 6
\][/tex]
Thus, the equation in terms of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] becomes:
[tex]\[
a + b = c
\][/tex]
where:
[tex]\[
\frac{350}{x + 20} + \frac{350}{x - 20} = 6
\][/tex]
Now, let's explicitly state [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
[tex]\[
a = \frac{350}{x + 20}, \quad b = \frac{350}{x - 20}, \quad c = 6
\][/tex]
Inserting the values into the final form:
[tex]\(
\boxed{
\frac{350}{x + 20} + \frac{350}{x - 20} = 6
}
\)[/tex]
This is the correct equation that describes the situation.
