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Australian AMC 2011 - Intermediate Question 28

AMC AUSTRALIA · Australian AMC 2011 - Intermediate

Question 28

Two beetles sit at the vertices $A$ and $H$ of a cube $ABCDEFGH$ with edge length $40\sqrt{110}$ units. The beetles start moving simultaneously along $AC$ and $HF$ with the speed of the first beetle twice that of the other one.

Question illustration

What will be the shortest distance between the beetles?