# Races and Circular Tracks

Adam and Bob are running on a circular track of circumference 1500 m. They start simultaneously from point A in the same direction. Ratio of their speeds is 5:3 respectively. If they keep running , then at how many different points can they meet?

a)Two b)One c)Three d)Data Insufficient

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Do you have any thoughts on the problem? Have you found any points where they can meet? If you know one time when they meet, can you find another time when they meet? I added the alg-precalc tag. – Gerry Myerson Jul 25 '12 at 6:14
So, are these runners running forever? Is that what you mean by "keep running"? – dc631 Jul 25 '12 at 6:14
@Dylon: I have converted your answer to a comment. Answers should be reserved for posts that answer the question. But because you do not have 50 reputation points yet, you can only comment on your own questions and answers. So, you didn't do anything wrong; the "add comment" button will only appear for you once you gain 50 points. Here is an explanation of reputation points. – Zev Chonoles Jul 25 '12 at 6:16

Hint: convert $1500\ m \rightarrow 2\pi$ and work some trigonometric magic. The two runners meet when the difference in their phases ($5t-3t$) is a multiple of $2\pi$. You still have to find all positions, however...