Here's my attempt.
let slower guy make n laps his vel = 1/10 lap/min
then,faster guy makes n+2 laps his vel = 1/6 lap/min
time taken for this is same for both guys.
n/ (1/10) = (n+2)/(1/6)
n=3 , slower guy makes 3 laps, takes 3*10 = 30 mins.
The LCM method is much quicker.
LCM of 6 and 10 gives the time when both guys meet at a point and complete an Integer number of laps.
The edit function has come back ......thank god...( or actually the programmer)
I'm crossing the bridge.........