Blocked people appearing on main timeline?

When I block a person, I want to be able to hide their tweets from the main timeline/searches. Every time I click a trending topic, for example, there are hundreds of spam tweets from the same handful of people. It makes it utterly impossible to actually see what the trending topic is all about. I don't care if they are trying to follow me or not, they are ruining the experience of trying to navigate Twitter. This is a serious problem and makes me want to stop using the site. Please make blocked users disappear from the timeline and searches.