OK, how would libertarians deal with existing public roads?
It is my opinion that Libertarians would deal with existing public roads pretty much the way the D and Rs do (just a little more openly about it). Of course their are a number of end state solutions, as well as interim state solutions that are being advocated, which caucuses will argue over and refine as the movement grows. Since I do not agree with the most popular of the end state solutions, which are the ones most often written about, I'm not the one to give a presentation on them. Besides, I'm not going to do your homework for you. But nor will I pass up an opportunity to argue the merits of one proposal over another.
There is one comment, I'm biting my tongue to make since you raised the question. Much of the popular libertarian theory says (or at least suggests), that the government has no right to own land, roads, or highways. While I've read a lot arguments on how it would be better if the government didn't own such, I've yet to see a principled argument against such ownership. I've also not seen a nondependent on other factors argument for such privatization.
Use taxes.
[got any other real tough ones, roscoe?]