Hi I have some questions about back links, how long does it take for the search engines to rank you based on the quality backlinks you have to your site since the first time they link to you. And also, the page rank that is pass trough the backlinks, is it just for the particular page that it is link to, or is it affect all the other pages in the site. Thanks
The PR, is for the page the link is pointing to. As for quality backlinks and ranks, it depends on a few factors such as: Google must index the page your are listed on Google must index the page the link is pointing too or cache it and then they will update the ir SERP
There isn't a strict time-line that you can identify. As Camay points out, there are several pages that must be cached first before any rankings can be assigned. The speed of this process depends on how frequently Google crawls both your site and the site where the link is coming from - and this frequency can vary wildly from a few days to several months. As for passing the link juice to other pages, yes the page receiving the link can pass the the PR juice to other pages of the site. In fact is has been speculated that domains are assigned a "value" based on the total number of in-bound links.
It is difficult to estimate time for page rank but u keep working for backlinks u will get the difference in pagerank definately.
I think it affect all the other pages that is in your site as well. It probably took 3-4 days for the search engine to get you rank. Get more quality backlinks do help improve your PR