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?

• Assuming that the first phase, during which father runs and son walks, lasts ‘x’ minutes, and the second phase ‘y’ minutes, we get two equations:
  x + y = 45 and 5x + 2y = 4x + 10 y
  Solving the above equations we find that ‘x’ equals 40 minutes and ‘y’ 5.
  Thus father runs for 40 minutes. As the ratio of their speeds in the first phase.is 5:4 the two meet along the side opposite the start point after father has covered two thirds of that side and son one-third.
• 13 years agoHelpfull: Yes(4) No(1)
• the father runs for 40 min, walks for 5 min
  totally they walks/runs a distance of 3.5 mile, crosses after 23 min 20 sec. after father has covered 1.99 miles
• 13 years agoHelpfull: Yes(0) No(0)