I was curious as to what the difference between web and worker dynos is on Heroku. They give a one sentence explanation on their pricing page, but this just left me confused
https://stackoverflow.com/a/19965981/1233555 - Heroku has gone to random routing, so some dynos can have queues stacking up (while they serve a lengthy request) while other dynos are free. Avoid this by making sure that all requests are handled very quickly in your web dynos. This will reduce the number of web dynos you need, while requiring more worker dynos.
You also need to care about your web app supporting concurrency, which only some Rails configs do - try Unicorn, or carefully-written code (for I/O that doesn't block the EventMachine) with Thin.
You probably have to try, rather than calculate, to see how many dynos of each kind you need. Make sure their New Relic reports the dyno queue - see the above link.