Answer:
Race 1: Brian, Charlie, Alan, Darren.
Race 2: Charlie, Darren, Alan, Brian.
To explain - since Charlie always beat Darren and Darren had a second place, one race must have been Charlie first and Darren second. Brian therefore won the other race with Charlie second. Since only one runner finished in the same place in both races, this must have been Alan in third. QED.