That's why I use google appengine. It would have handled what you describe without even going over the daily free limit. Of course, you wouldn't be cool as rails.
In the free configuration, I've clocked it between 4 and 6 seconds. (Sometimes up to 10 seconds, but not recently.) With the 1.4.0 release of the App Engine SDK, the cold start time has become less important, though. First, you can pay $9/month to have three instances running all the time. Second, App Engine can send a "warmup" request to your application.