You need to use WINDOW_MAX() in the expression to find the id. Too hard to explain more from my phone.
I didn't understand how to use WINDOW_MAX to solve this, but I found a separate forum thread ( http://community.tableau.com/thread/113309 ) that covered this problem. I was able to use Joe Mako's approach:
1. Put "ID" on the Level of Detail shelf and add a Sort, set to Descending on the field Duration (Time) with an aggregation of "Max".
2. Create a calcuated field called IsFirst with the formula:FIRST()==0
3. Place IsFirst on the Level of Detail shelf and set it to Compute using ID
4. Ctrl-drag-and-drop IsFirst from Level of Detail to Filter, and only keep True