20. As shown in the figure, $P$ is a point on the side $AB$ of a regular hexagon $A B C D E F$, $P M / / C D$ intersects $E F$ at $M$, and $P N / / B C$ intersects $C D$ at $N$. A red and a blue sprite start from point $N$ at the same time and walk along the perimeter of pentagon $N P M E D$ and hexagon $C B A F E D$ at a uniform speed, respectively, and return to point $N$ at the same time after each completes one round. What is the ratio of the blue sprite's speed to the red sprite's speed?
20. As shown in the figure, $P$ is a point on the side $AB$ of the regular hexagon $A B C D E F$, $P M / / C D$ intersects $E F$ at $M$, and $P N / / B C$ intersects $C D$ at $N$. Two small sprites, one red and one blue, start from point $N$ at the same time and walk along the perimeter of the pentagon $N P M E D$ and the perimeter of the hexagon $C B A F E D$ at a uniform speed, each completing one round and returning to point $N$ at the same time. What is the ratio of the blue sprite's speed to the red sprite's speed? [Analysis] First, determine the distances traveled by the blue and red sprites, then the ratio of their speeds is equal to the ratio of their distances, which will lead to the conclusion.
[Solution] Solution: As shown in the figure,
Let the side length of the regular hexagon be $a$,
Then the distance the blue sprite travels in one round is $6 a$,
Connect $B E$ to intersect $P N$ at $H$, and draw $A O / / E F$,
Therefore, quadrilateral $M E O G$ is a parallelogram, $B C N H$ is a parallelogram, and $\triangle P B H$ is an equilateral triangle,
Therefore, $A F=M G, A G=P G=A P, B P=P H, B H=C N$,
The distance the red sprite travels in one round is $M P+P N+N D+D E$
$$
\begin{array}{l}
=M G+P G+P H+N H+N D+D E \\
=A F+A P+B P+B C+C N+D N+D E \\
=A F+A B+B C+C D+D E \\
=5 a,
\end{array}
$$

Therefore, the blue sprite's speed is $\frac{6}{5}=1.2$ times the red sprite's speed.
Answer: The blue sprite's speed is 1.2 times the red sprite's speed.