A father and his son go out for a ‘walk-and-run’ every morning around a track formed by an equilateral triangle. The father’s walking speed is 2 mph and his running speed is 5 mph. The son’s walking and running speeds are twice that of his father. Both start together from one apex of the triangle, the son going clockwise and the father anti-clockwise. Initially the father runs and the son walks for a certain period of time. Thereafter, as soon as the father starts walking, the son starts running. Both complete the course in 45 minutes. For how long does the father run? Where do the two cross each other?

• suppose side of triangle is a. then total distance is 3a.
  now suppose father runs for x min so.
  5x+2(45-x)=3a
  4x+10(45-x)=3a
  by above eq. x=40 min.
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