Ants released from both ends of a string

Two people stand at opposite ends of a very thin string. One releases $40$ ants that crawl towards the other end, and the other releases $80$ ants that crawl towards the first person. Ants keep moving forward, but whenever two meet they both reverse. Let $x$ be the number of ants that arrive at the first person (who released $40$) and $y$ the number arriving at the second person. What is $x-y$?

$40$. A head-on bounce is indistinguishable from the two ants passing through each other, so count trajectories as if ants ghost through: all $80$ trajectories heading towards the first person reach her and all $40$ heading the other way reach the second, so $x-y=80-40=40$.