I agree with the other posters that a minute before collision, the first missile is (21,000 miles per hour)*(1 hour per 60 minutes)*(1 minute) = 350 miles from the point of collision, and the second is (9,000 miles per hour)*(1 hour per 60 minutes)*(1 minute) = 150 miles from the point of collision. However:
We've been told that the missiles were "set on a collision course", but have not been told the angle at which they were set to collide. It matters. If they're on opposite paths (i.e. set to have a nose-to-nose collision), they are (350 miles) + (150 miles) = 500 miles from each other. If they are on identical paths (i.e. set to have a nose-to-tail collision), they are (350 miles) - (150 miles) = 200 miles from each other.
More generally, the distance between them a minute before collision can be found using the Law of Cosines
. If θ is the angle of collision, the distance a minute before collision is ((350 miles)2
+ (150 miles)2
- 2(350 miles)(150 miles)(cos θ))0.5
= 100*(14.5 - 10.5(cos θ))0.5
(All that assumes, of course, that they're following linear trajectories. Since their starting distance from one another implies that they are ICBMs, this is not a good assumption; it is more likely that they are following elliptical trajectories, which further complicates the situation. However, "500 miles" will still be the upper bound.)