Two boats start together and race across a $44-$km$-$wide lake and back. Boat A goes across at $44$ km$/$h and returns at $44$ km$/$h$.$ Boat B goes across at $22$ km$/$h$,$ and its crew, realizing how far behind it is getting, returns at $66$ km$/$h$.$ Turnaround times are negligible, and the boat that completes the round trip first wins.

$($a$)$ Which boat wins? $($Or is it a tie?$)$

by how much in km$?$ What is the average velocity of the winning boat in km$/$h$?$