14. (15 points) As shown in the figure, $A$, $B$, and $C$ are the north gate, west gate, and east gate of a school, respectively. On the map, segments $AD$, $AE$, and $DE$ are all roads. Points $B$ and $C$ are on $AD$ and $AE$, respectively, and $DC$ and $BE$ intersect at point $P$. The areas of $\triangle PBC$, $\triangle PBD$, and $\triangle PCE$ are 73000 square meters, 163000 square meters, and 694000 square meters, respectively. Xiaoye and Xiaofeng walk at the same speed. One day, after school, they both start from the north gate at the same time. Xiaoye runs first and then walks, while Xiaofeng walks all the way. When Xiaoye runs to the west gate in 3 minutes, Xiaofeng has just walked to the east gate. Xiaoye continues to run to point $D$ in 8 minutes, then walks along $DE$ to meet Xiaofeng, who walks from the east gate to $E$ and then to $D$. The next day, following the same travel method, if Xiaofeng wants to meet Xiaoye at the midpoint of the $DE$ road, how many minutes earlier should Xiaofeng start compared to Xiaoye?
【Analysis】First, analyze the proportional relationships between the line segments, find the relationship between the distances of the two segments, and take the difference.

【Solution】Solution: According to the problem, we have:
$$
\frac{A B}{B D}=\frac{3}{8}, \frac{C E}{C A}=\frac{S_{\triangle B C E}}{S_{\triangle B A C}}=\frac{S_{\triangle B C E}}{S_{\triangle B C D}} \cdot \frac{B D}{A B}=\frac{73000+694000}{73000+163000} \times \frac{8}{3}=\frac{26}{3} ;
$$

Therefore, it takes Xiao Feng 26 minutes to walk $C E$. If Xiao Feng wants to meet Xiao Ye at the midpoint of the $D E$ segment, Xiao Ye needs to start 26 - 8 = 18 (minutes) earlier.

Answer: If Xiao Feng wants to meet Xiao Ye at the midpoint of the $D E$ segment, he needs to start 18 minutes earlier than Xiao Ye.