question from the australian maths competition (1 Viewer)

bleakarcher

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A cube of side length 400sqrt(11) has vertices A,B,C,D,E,F,G,H. Two beetles lie on the same face of the cube on the vertices, one above the other. One beetle begins to travel downwards towards the base of the square surface at twice the rate at which the remaining beetle travels to travel up towards the top edge of the square surface. Find the minimum distance between the two beetles, assuming the begin their journeys at the same time.

btw my answer was 420 units
 

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