Why isn't my TimeSpan.Add() working?

There has to be an easy answer:

var totalTime = TimeSpan.Zero;

foreach (var timesheet in timeSheets)
{
   //assume "time" is a correct, positive TimeSpan
   var time = timesheet.EndTime - timesheet.StartTime;
   totalTime.Add(time);
}

There's only one value in the list timeSheets and it is a positive TimeSpan (verified on local inspection).