Roger can run one mile in 14 minutes. jeff can run one mile in 12 minutes. if jeff gives roger a 1 minute head start, how long will it take before jeff catches up to roger? how far will each have run?

Let the time taken by Roger = x minutes
 Speed of Roger = (1/12)
 Distance covered by Roger =(x)/12 (1)

   Time taken by Jeff = x+1 minutes
 Speed of Jeff = (1/14)
 Distance covered by Jeff =(x+1)/14 (2)

     Distance covered by Jeff = Distance covered by Roger

   (x+1)/14 = x/12
 12x +12 = 14x
  2x = 12
  x=6
 Substitute the value of x in equation (1),
 Distance covered = x/12 = 6/12 = 1/2
  Time taken by Jeff to catch up to Roger is 7 minutes
 Distance covered by them = 1/2 mile