<h2>
Hello!</h2>
The answer is:
It will took 0.375 hours for Ava and Kelly to be 3/4 miles apart.
<h2>
Why?</h2>
To calculate how long after they start they will be 3/4 miles apart, we need to write two equations.
So, writing the equations, we have:
Calculations for Ava:
We have the following information,
![v_{Ava}=6mph](https://tex.z-dn.net/?f=v_%7BAva%7D%3D6mph)
Then, writing the equation,
![x_{Ava}=x_{o}+v_{Ava}*t](https://tex.z-dn.net/?f=x_%7BAva%7D%3Dx_%7Bo%7D%2Bv_%7BAva%7D%2At)
![x_{Ava}=x_{o}+v_{6mph}*t](https://tex.z-dn.net/?f=x_%7BAva%7D%3Dx_%7Bo%7D%2Bv_%7B6mph%7D%2At)
Calculations for Kelly:
We have the following information,
![v_{Kelly}=8mph](https://tex.z-dn.net/?f=v_%7BKelly%7D%3D8mph)
We need to calculate when Kelly will be 3/4 miles apart of Ava, so, it's position will be the Ava's position plus 3/4 miles.
Then, writing the equation,
![x_{Ava}+0.75miles=x_{o}+v_{Kelly}*t](https://tex.z-dn.net/?f=x_%7BAva%7D%2B0.75miles%3Dx_%7Bo%7D%2Bv_%7BKelly%7D%2At)
![x_{Ava}+0.75miles=x_{o}+v_{8mph}*t](https://tex.z-dn.net/?f=x_%7BAva%7D%2B0.75miles%3Dx_%7Bo%7D%2Bv_%7B8mph%7D%2At)
Now, substituting Ava's speed into the second equation, we have:
![x_{o}+6mph*t+0.75miles=x_{o}+8mph*t](https://tex.z-dn.net/?f=x_%7Bo%7D%2B6mph%2At%2B0.75miles%3Dx_%7Bo%7D%2B8mph%2At)
![6mph*t+0.75miles=+8mph*t](https://tex.z-dn.net/?f=6mph%2At%2B0.75miles%3D%2B8mph%2At)
![8mph*t-6mph*t=0.75miles](https://tex.z-dn.net/?f=8mph%2At-6mph%2At%3D0.75miles)
![2mph*t=0.75miles](https://tex.z-dn.net/?f=2mph%2At%3D0.75miles)
![t=\frac{0.75miles}{2mph}=0.375hours](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B0.75miles%7D%7B2mph%7D%3D0.375hours)
Hence, we have that it will took 0.375 hours for Ava and Kelly to be 3/4 miles apart.
Have a nice day!