Two friends A and B simultaneously start running around a circular track in the same direction. A travels at 6m/s and B runs at b m/s. If they cross each other at exactly two points on the circular track and b is a natural number less than 30, What are the possible values of b ?

• I think b is 18 m/s .
  length of track is 720 m (say).
  A covers 1/2 track in 720/(6*2) = 60 secs or 1 min.
  In 1 min, B covers 18*60 = 1080 mtrs = 1.5*760 = 1.5 track.
  
  so A and B will meet at centre of track.
  Next time , they will meet at starting point when A has completed one round and B has covered 3 rounds.
  
  and so on..
• 12 years agoHelpfull: Yes(5) No(4)
• Ans is 3
  let track length b T,
  time taken to meet for the first time =T/(relative speed)=T/(6-b)
  time taken by A=T/6
  time taken by B=T/b
  so,time taken to meet for the first time at starting point =Lcm(T/6,T/b)=T/Hcf(6,b)=2....so 2,10,18
• 7 years agoHelpfull: Yes(0) No(0)