Answer:
a) It will take you 16.94 min to climb the stairs.
b) The numbers of flights are 123 flights. 
Explanation:
a) Let the energy consumption while climbing the stairs be 685 W in kcal/min is given by:
rate of energy consumption = (685 W)×[(0.01433kcal/min)/1 W]
                                                = 9.81605 kcal/min
the time it takes to climb the stairs is given by:
t = E/P
  = (166.0 kcal)/(9.8 kcal/min)
  = 16.94 min
Therefore, it will take you 16.94 min to climb the stairs.
b) Given t is the time it takes to climb stairs and N is the number of stairs to climb per min, then the number of stairs is:
n = t×N
   = (16.94)×(116)
   = 1965 stairs
given the number of stairs each flight as N1, then the number of flights is given by:
flights = n/N1
           = (1965)/(16)
           = 123 flights
Therefore, the numbers of flights are 123 flights.