# 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

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...

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-1. No trigonometry is needed to solve this problem. No Greek letters either. Let's not over-complicate. – user22805 Jul 25 '12 at 8:35

Adam and Bob meet when Adam is ahead by an integer number of laps. When Bob has run 3 laps, Adam has run 5 and they both meet back at the starting location. The question is where do they meet when Adam is one lap ahead?

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