About tall people issues

Is Bézout theorem necessary for this ? Apart from that or brute force, I’m not sure how to start.

And I’m not sure why this is called "about tall people issues" either !

Yes you need to use Bézout for this one, but I guess brute force can also work maybe, however the proof of minimality won’t me easy.
Another way to rephrase the problem is to seek for two integers $a,b$ such that $11a+17b=9$ if you want.

And it is called this way because, as a tall person myself, it is not easy to make small steps while walking, so I need to make this kind of calculation when I’m walking with small people in order to not leave them too far behind :(