A man drives one-third of the distance home at 25 mi/h. How fast must he drive the rest of the way in order to average 35 mi/h for the entire trip?

If s represents the speed for the remainder of the trip, the total trip time is
  1/25 + 2/s = 3/35
  2/s = 3/35 - 1/25    (subtract 1/25)
  2/s = (75 - 35)/(35*25)    (compute the difference)
  2/s = 8/175    (reduce the fraction)
  s = 175/4    (multiply by 175s/8)

The man must average 43 3/4 mph the rest of the way.