I have heard similar things but I don't remember if it was 20 secs/mile. I don't have personal experience with it since I didn't lose any more weight after I started racing. But I think you would be better served by revising your training to do things like intervals, tempo runs and possibly hill repeats. Finding a coach or joining a running club might help to get advice on adjusting your training. If you want to look at some online stuff, try http://www.mcmillanrunning.com/.
Good luck.