Answer :

         If t : time for Mario to run 10 m and  Luigi for 7 m.
         Calculate time of Mario " x " to complete his 13 m : (10 / t) = (13 / x) <==> x = 1,3t
         Calculate time for Luigi " y " to complete 10 m : (7 / t) = (10 / y) <==> y = 1,43t
         Mario wins by about  (1,43t - 1,3t) = 0,13t