There is a OOTB Report that does a similar function as you described.
Launch Case Manager portal and open the Report browser. In "Monitor Assignments" Public category, open "Timeliness by work queue" Report.
This Report will group by the workbasket the operator belongs to. When you click on any particular workbasket, a drill down report will be shown. Here the Work objects corresponding to the assignment routed to the work queue and Date time of when it was assigned will be available.
To understand the configuration, open the report definitions in designer studio and achieve your implementation.
pyAgeByWorkQueue ( Timeliness by work queue ) and pyDrillToDetails ( Workbasket Drilldown Details )