Follow me here.

One of the most famous lines is Elwood's "It's 106 miles to Chicago...."

Now, we don't know what time the show started at the Palace Hotel ballroom, and they WERE late, but let's conservatively estimate the show starting at 9 PM. Let's guess Jake and Elwood are 2 hours late. So they go on at 11. They do 2 songs and bolt. They escape, get shot at by Carrie Fisher, then leave. Let's say it's midnight.

They are traveling at top speed, and get into Chicago late enough for a government office to be open. The office probably opens at 8 AM.

So it took them 8 hours to go 106 miles at top speed?

That's some detour!