# 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

-
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...