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IMAS 2011 Junior Division — Second Round Question 6

IMAS · IMAS 2011 Junior Division — Second Round

Question 6

The diagram shows a city block (shaded). Peter starts from $A$ and moves to the east while Toney starts from $A$ and moves to the south. They both follow the perimeter of the city block, and eventually meet at the point $D$ on the side $BC$, 2 km from $C$. If the constant speed of the Toney is $\frac34$ of the constant speed of the Peter, what is the length of the zig-zag line from $A$ to $C$?

Question illustration

Give the answer in km.