Racing laps equation

Question

Competior A laps a circuit in 76 seconds Competitor B laps a circuit in 92 seconds. 

 

there is a race of  say 10 laps - at what point will competitor A "Lap" competitor B  (eg 5.4 laps).

 

What is the equation so it can be also worked out  for any competitor when seconds per lap change?

 

Thanks

Answer 1

Let competitor A's speed be La = 1/x (laps/sec) and competitor B's speed be Lb = 1/y (laps/sec). The laps traveled by A,La is 1/x*t=La (laps/sec*laps), and the laps traveled by B, Lb=1/y*t with t (sec) the time from starting. They will lap each other at the same time say t1. Then equating laps La*1/y*t1=Lb*1/x*t1 or La/Lb= y/x, Lb/La=x/y . From the problem definition x=76 (1/76 laps per sec) and y=92. Then A will lap B in 92/76 laps.