I supposed it depends where your client is located. In the US northeast, a senior developer makes around $50-80/hr. I've done a few fix rate Rails projects that took about 20-30 hours in all for about $5k, so around $25/hr.
Your math is right, but his suggestion is wrong. No way should he charge $250. That's crazy, unless you are in the top 1% in mobile apps. Even then is sounds a little high.
Completely agree - but it does bring up an interesting point: bidding on projects at a fixed rate can lead to higher hourly rates (although definitely not always, especially for someone just starting).