"There are search parameters too in each of the tables"
What does that mean?
The Tasks have to be active and within the current time period, the Timesheets, people need to be from a certain department, the Resources actually don't need to be searched.
It sounds like two separate reports, one with Task as the primary sort showing the summarized data by people and the other with People as the primary sort, showing the detail by task.
I ran across this page and thought of this discussion. It sounds like a 'join table' might be the right solution. http://help.filemaker.com/app/answers/detail/a_id/9922