A ‘figure of eight’ track is constructed from two circles: a large circle of radius 2 units and a small circle of radius 1 unit. Two cars X, Y start out from the positions shown: X at the top of the large circular part and Y at the bottom of the small circular part. Each car travels round the complete circuit in the directions shown by the arrows. If Y travels twice as fast as X, how far must X travel before the cars collide? Give your answer as an exact value.
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Junior Mathematical Olympiad 2011 (2011)
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