Let's solve this step by step.
We are given:
- The distance for each leg of the trip is 350 miles.
- The total trip time is 6 hours.
- The wind speed is 20 miles per hour.
- The speed of the airplane in still air is x.
First, let's write down the key points:
1. Speed of the airplane with the wind:
[tex]\[ \text{Speed with wind} = x + 20 \][/tex]
2. Speed of the airplane against the wind:
[tex]\[ \text{Speed against wind} = x - 20 \][/tex]
Next, let's define the time taken for each part of the trip. The time to travel a distance can be found using the formula:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \][/tex]
3. Time to travel to the destination with the wind:
[tex]\[ \text{Time to destination} = \frac{350}{x + 20} \][/tex]
4. Time to return against the wind:
[tex]\[ \text{Time back} = \frac{350}{x - 20} \][/tex]
The total time for the round trip is the sum of these two times and is given as 6 hours:
[tex]\[ \frac{350}{x + 20} + \frac{350}{x - 20} = 6 \][/tex]
Now, let’s substitute the values in the expression:
[tex]\[ a = 350 \][/tex]
[tex]\[ b = 20 \][/tex]
[tex]\[ c = 6 \][/tex]
Thus, the equation that describes this situation is:
[tex]\[ \frac{a}{x + b} + \frac{a}{x - b} = c \][/tex]
Or more specifically:
[tex]\[ \frac{350}{x + 20} + \frac{350}{x - 20} = 6 \][/tex]
Here, the values are:
[tex]\[ a = 350, b = 20, c = 6 \][/tex]
So, replacing [tex]\( a \)[/tex] and [tex]\( b \)[/tex] in the given equation format [tex]\( \frac{a}{x+b} \quad \frac{a}{x-b} \)[/tex]:
[tex]\[ \frac{350}{x+20} \quad \frac{350}{x-20} \][/tex]
Therefore, the corrected equation is
[tex]\[ \frac{350}{x + 20} + \frac{350}{x - 20} = 6 \][/tex]
