how much time to a web site for PR 1?

[Jake]

Actually page rank seems to be mainly effected by the number and power of incoming links, I believe an active site might hit pr1 in a couple months, although it has become harder than a few years ago.

Be aware that Google only updates page rank about 5 times a year, less frequently lately, s the fruits of your effort may not immediately be apparent.

There was nearly 10 months of no update before the last Nov 29, 2013 update, this should be taken as a sign that Google has depreciated PR.

http://www.hobo-web.co.uk/google-pr-update/