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:
![s = \frac{d}{t}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7Bd%7D%7Bt%7D)
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 ![d = 320](https://tex.z-dn.net/?f=d%20%3D%20320)
Then
![s = \frac{320}{t}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B320%7D%7Bt%7D)
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.
![s - 6 = \frac{280}{t}](https://tex.z-dn.net/?f=s%20-%206%20%3D%20%5Cfrac%7B280%7D%7Bt%7D)
From the first equation:
![s = \frac{320}{t}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B320%7D%7Bt%7D)
![st = 320](https://tex.z-dn.net/?f=st%20%3D%20320)
![t = \frac{320}{s}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B320%7D%7Bs%7D)
Replacing:
![s - 6 = \frac{280}{t}](https://tex.z-dn.net/?f=s%20-%206%20%3D%20%5Cfrac%7B280%7D%7Bt%7D)
![s - 6 = \frac{280}{\frac{320}{s}}](https://tex.z-dn.net/?f=s%20-%206%20%3D%20%5Cfrac%7B280%7D%7B%5Cfrac%7B320%7D%7Bs%7D%7D)
![320(s - 6) = 280s](https://tex.z-dn.net/?f=320%28s%20-%206%29%20%3D%20280s)
![320s - 1920 = 280s](https://tex.z-dn.net/?f=320s%20-%201920%20%3D%20280s)
![40s = 1920](https://tex.z-dn.net/?f=40s%20%3D%201920)
![s = \frac{1920}{40}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B1920%7D%7B40%7D)
![s = 48](https://tex.z-dn.net/?f=s%20%3D%2048)
Her average speed is 48 miles per hour.