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UKMT Intermediate Mathematical Challenge, 2024

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows a regular hexagon $RSTUVW$ . The area of the shaded pentagon $RSTPQ$ is one quarter of the area of the hexagon. Jay and Kay walk around the hexagon from $P$ to $Q$ , Jay going clockwise and Kay anticlockwise. What is the ratio of the distance Jay walks to the distance Kay walks?

(A) $1:2$ (B) $2:3$ (C) $3:5$ (D) $4:7$ (E) $5:8$

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