How can I find the fastest path by car to reach a US state from a given US location?

1. Open google maps
2. Get directions by car from your starting point to somewhere (anywhere) in your target state
3. Slowly drag the destination marker around along the state borders and watch the duration shown in the tooltip
4. Use your mind to keep track of when the duration is lowest
5. You have found your answer

This has been something that I have often wished existed (although for me it's usually at the US county level). I don't have a perfect solution, but I do have one that in practice works fairly well. In other words, if your goal is a systematic solution a la a mathematical proof, this isn't the answer you're looking for. On the other hand, if you just want a functional answer, I think this one's usually good enough.

Let's say that you're in Mason City, IA, and you want to get to Illinois (I chose one that's kind of diagonal to make it interesting).

• By eye draw a line from Mason city to the IL border
• Look around and find 3-5 cities across the border near that location on the map. I chose Rockford, Sterling, and Moline. (first image)
• Use google maps to find directions to each of those locations. Note the border crossing in each case. (second image)
• Find directions from the starting point to the border crossing in each case. The times to the border for me were: Rockford: 2:47, Sterling: 3:31, Moline: 3:28. The route to Rockford wins.
• Now we have a pretty good idea that the US-20 bridge on the Mississippi river in Dubuque is probably the fastest way to the border. That said, one could continue to iterate by choosing more cities this time all very close to Dubuque. (You generally only have to do this in the eastern US where roads are laid out less systematically.