Integrate a Rails application into a site made in wordpress
You might want to check out this plugin for wordpress:
http://wordpress.org/extend/plugins/rails-integration-api/
It basically copies any 3rd party app (such as Wordpress) to a subdirectory of your Rails app.
The real challenges are in the details.... authentication, authorization between admins in the WP site and the Rails app, etc. A question you should ask yourself is how much are the website(wp) and Rails app going to need to talk to each other, if at all?
However, if the WP site is just used mostly as an informational site or maybe a blog, you can place your WP site inside the /public directory of your rails app, tweak the config files (if you're running Apache/Passenger etc), and go from there.