You will sooner than you think, just keep putting the miles in, but you do need rest days for the body to recover.
Apart from my first ride and short commutes, most of my rides have been 20+ miles since I started in June, however the first rides wern't fast and frequent stops, I can do 30+ with out stopping though I do general stop about half way, or the top of hill sometimes. I am not fast even now compared with some, but I avg about 13.5mph, yesterday was slow but it was half a commute and to be honest, I just couldn't get going, but I had just done 140 miles in the previous 5 days.So just keep at it, you will get fitter and stronge
r (though its not about strength).