The answers to those questions definitely depend on your environment.

What version of SQL Server is it?

Is this machine a production application database? Or a datawarehouse?

If you have investigated the logs and the execution times are all fast then moving the Reporting Services to a different server is not going to help you. You really need to look at why the reports are taking a long time.

Take one really long report as an example, and look at its records in the execution log tables and tell me what you see there. Are the reports running on subscription? Could caching their execution help? Are they many many pages long? Are they slow to render on screen (could be an interactive size setting issue) or slow to export to another format?

I recommend finding the cause of the issue rather than changing your infrastructure in the hope that the problem will go away.