Two contestants run a $3-kilometre$ race along a circular course of length $300$ $metres$. If there speeds are in the ratio of$ 4:3$, how often and where would the winner pass the other? (The initial start-off is not counted as passing.) (A) $4 $ times; at the starting point. (B) Twice; at the starting point. (C) Twice; at a distance of $225 $ metres from the starting point. (D) Twice; once at $75 metres$ and again at $225 $ metres from the starting point.
I have solved it in the following way: The race is a total of $10 $ laps ($3km / 300m = 10 $ laps)The faster runner will complete $4 $ laps in the same time the slower runner completes $3 laps$, so they will meet after $4 laps$ and again after $8 $ laps. The faster runner will then complete the race while the slower runner still has $2½$ laps to go. Answer:$ B $ Twice (after 4 laps and 8 laps, at the starting point of each lap)
But i am looking for a more definite and clear method. Any help will be appreciated!