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So it might take a month, or it might take a year.
Remember, search engines rank URLs -- Not pages and not sites.
Oh and do put more effort into your pages than just title and <H1> tags -- Good content draws free inbound links, and a good and unique meta description can greatly affect your click-through rate in search results.
On the other hand, a non-unique meta description can throw your page into what we used to term the Supplemental index if other on-page factors are also weak, and you don't want to be there.