Fly shuttling once between two approaching cars

Two cars start at the opposite ends of a straight $400$-mile road and head toward each other, the first at $120$ mph and the second at $60$ mph. At the start, a fly leaves the second car and flies at $180$ mph toward the first car; on touching it, the fly turns straight round and flies back toward the second car at the same speed. To the nearest minute, how long after the start does the fly get back to the second car?

$120$ minutes. The fly and the first car close at $180+120=300$ mph, meeting after $\tfrac{400}{300}$ h $=80$ min, when the cars are $400-180\cdot\tfrac43=160$ miles apart. The fly and the second car then close at $180+60=240$ mph, taking $40$ more minutes, for $120$ in total.