Two friends A and B run around a circular track of length 510 metres, starting from the same point, simultaneously and in the same direction. A who runs faster laps B in the middle of the 5th round. If A and B were to run a 3 km race long race, how much start, in terms of distance, should A give B so that they finish the race in a dead heat?

• A and B run around a circular track. A laps B in the middle of the 5th lap. i.e. when A has run four and a half laps he has covered a distance which is 1 lap greater than that covered by B's.
  
  Therefore, when A runs 9/2 laps, B runs 7/2 laps.
  
  This is same as saying when A runs 9 laps, B runs 7 laps.
  
  i.e in a race that is 9 laps long, A can give B a start of 2 laps.
  
  So, if the race is of 3000 metres long, then A can give B a start of
  (2/9)×3000= 666.67 metres.
• 7 years agoHelpfull: Yes(0) No(0)