Answer :
Answer:
Her average speed is 48 miles per hour.
Step-by-step explanation:
We solve this question using a system of equations.
The speed equation is:
[tex]s = \frac{d}{t}[/tex]
In which s is the speed, d is the distance, and t is the time.
Gabriella drives her car 320 miles and averages a certain speed.
So [tex]d = 320[/tex]
Then
[tex]s = \frac{320}{t}[/tex]
If the average speed has been 6 miles less she could have traveled only 280 miles in the same length of time.
So, which s - 6, d = 280.
[tex]s - 6 = \frac{280}{t}[/tex]
From the first equation:
[tex]s = \frac{320}{t}[/tex]
[tex]st = 320[/tex]
[tex]t = \frac{320}{s}[/tex]
Replacing:
[tex]s - 6 = \frac{280}{t}[/tex]
[tex]s - 6 = \frac{280}{\frac{320}{s}}[/tex]
[tex]320(s - 6) = 280s[/tex]
[tex]320s - 1920 = 280s[/tex]
[tex]40s = 1920[/tex]
[tex]s = \frac{1920}{40}[/tex]
[tex]s = 48[/tex]
Her average speed is 48 miles per hour.