Put posts under same folder as Posts page

My site has a static front page, and the posts are on a page under /blog/, however when I create a post, they go under the root of the site such as http://www.example.com/hello-world/. I want them to go under http://www.example.com/blog/hello-world/, in order to keep things clean and to prevent any posts from conflicting with pages.

It’s set up as the #3 model here:
http://codex.wordpress.org/Creating_a_Static_Front_Page

I’ve been searching for a while, but haven’t found anything about how to do this. Is there a way to update the permalinks to include the folder of the posts page?