It seems the site is using WEBrick as the webserver. Replacing it with Thin should help a lot performance wise. Heroku has as section in their docs on how to change that: https://devcenter.heroku.com/articles/rails3#webserver

Also, letting the application serve all the static assets has an even bigger impact on the number of dynos you need. I'm not a heroku user, but it seems there are some good solutions to this problem, like https://devcenter.heroku.com/articles/cdn-asset-host-rails31