A driver of a red Lamborghini drives fast moving at $120$ km$/$h on a temporary one$-$way crossing. He observes that $75$ m ahead a yellow school bus is approaching from the opposite direction with a speed of $80$ km$/$h$.$ Immediately, both react by decelerating, the driver of the Lamborghini at a rate of $18$ m$/$s and the driver of the bus at a constant rate of $20$ m$/$s$.$

$1)$ Will they crash while moving? Justify

$2)$ If they collide, when and where do they collide?

$3)$ If they don't collide, what is the distance between them when one stops?