How fast does Google update its results?

That depends.

For the average website, about 3 weeks typically is enough for Google to have re-crawled and indexed your entire site.

For news, it is vastly different.

Here's an excellent report on how Google responded to the news of Bin Laden's death (and a comparison to how it operated 10 years ago):

Google & The Death of Osama Bin Laden

Quite a difference.