11. (12 points) The distance between locations $A$ and $B$ is 291 kilometers. Two people, Jia and Yi, start from $A$ and travel at a constant speed to $B$ at the same time, while Bing starts from $B$ and travels at a constant speed to $A$. When Yi has walked $p$ kilometers and meets Bing, Jia has walked $q$ kilometers. After some time, when Jia and Bing meet, Yi has walked a total of $r$ kilometers. If $p$, $q$, and $r$ are all prime numbers, then the sum of $p$, $q$, and $r$ is . $\qquad$
【Analysis】The key to this problem is to analyze the distance relationship between A, B, and C. In the two meetings, the speed remains unchanged, and the time of meeting is the same, so the speed ratio can be converted into the distance ratio.

【Solution】From the problem, we know $q293 . \therefore p>73$. The prime numbers between 73 and 97 are 79, 83, 89. When the last digit of $p$ is 9, the last digit of $q$ is 5, which does not meet the requirement.
$\therefore p=83$. Substituting $q=41$
$\therefore p+q+r=83+41+97=221$
In conclusion, the sum of $p, q, r$ is 221