Answer:
![h\:=\:\:\frac{-\pi \:kr\:+\:S}{\pi \:r}](https://tex.z-dn.net/?f=h%5C%3A%3D%5C%3A%5C%3A%5Cfrac%7B-%5Cpi%20%5C%3Akr%5C%3A%2B%5C%3AS%7D%7B%5Cpi%20%5C%3Ar%7D)
Step-by-step explanation:
Given the expression
![S=\pi \:r\left(h+k\right)\:](https://tex.z-dn.net/?f=S%3D%5Cpi%20%5C%3Ar%5Cleft%28h%2Bk%5Cright%29%5C%3A)
![S=\pi \:r\left(h+k\right)\:](https://tex.z-dn.net/?f=S%3D%5Cpi%20%5C%3Ar%5Cleft%28h%2Bk%5Cright%29%5C%3A)
Flip the equation
![\pi r\left(h+k\right)\:=\:S](https://tex.z-dn.net/?f=%5Cpi%20r%5Cleft%28h%2Bk%5Cright%29%5C%3A%3D%5C%3AS)
Apply distributive law: ![a\left(b+c\right)=ab+ac](https://tex.z-dn.net/?f=a%5Cleft%28b%2Bc%5Cright%29%3Dab%2Bac)
Add -πkr to both sides
![\pi hr+\pi kr+\left(-\pi kr\right)=S+\left(-\pi kr\right)](https://tex.z-dn.net/?f=%5Cpi%20hr%2B%5Cpi%20kr%2B%5Cleft%28-%5Cpi%20kr%5Cright%29%3DS%2B%5Cleft%28-%5Cpi%20kr%5Cright%29)
![\pi hr\:=\:-\pi kr\:+\:S](https://tex.z-dn.net/?f=%5Cpi%20hr%5C%3A%3D%5C%3A-%5Cpi%20kr%5C%3A%2B%5C%3AS)
Divide both sides by πr
![\pi hr\:/\:\pi r\:=\:\:\frac{-\pi \:kr\:+\:S}{\pi \:r}](https://tex.z-dn.net/?f=%5Cpi%20hr%5C%3A%2F%5C%3A%5Cpi%20r%5C%3A%3D%5C%3A%5C%3A%5Cfrac%7B-%5Cpi%20%5C%3Akr%5C%3A%2B%5C%3AS%7D%7B%5Cpi%20%5C%3Ar%7D)
![h\:=\:\:\frac{-\pi \:kr\:+\:S}{\pi \:r}](https://tex.z-dn.net/?f=h%5C%3A%3D%5C%3A%5C%3A%5Cfrac%7B-%5Cpi%20%5C%3Akr%5C%3A%2B%5C%3AS%7D%7B%5Cpi%20%5C%3Ar%7D)
Therefore, we conclude that:
![h\:=\:\:\frac{-\pi \:kr\:+\:S}{\pi \:r}](https://tex.z-dn.net/?f=h%5C%3A%3D%5C%3A%5C%3A%5Cfrac%7B-%5Cpi%20%5C%3Akr%5C%3A%2B%5C%3AS%7D%7B%5Cpi%20%5C%3Ar%7D)
It takes 8 hours to drive to Joliet, and that's 6 hours more than half the time it takes to drive to Davenport. So, I did 8-6 which equals 2. So 2 hours is half the time it takes to get to Davenport, which means it takes 4 hours to get to Davenport.