Collision Problems

Three interesting problems all including collisions, and all have a clever (and easily calculable) solution if you think about them:

(1) Two missiles speed towards each other at speeds of 130mph and 170mph. How far apart are they one minute before they collide?

(2) Two trains are 100 miles apart and they both steam towards each other at a constant speed of 50mph. A fly (who is incredibly fast) travels at the surreal speed of 60mph from the first train towards the second. When it reaches ithe train, it turns around. When it reaches the first train again, he turns around, and then it turns around and then.... It keeps on doing that until the trains collide. How far has it travelled when they eventually collide?

(3) What if it travels at 40mph?

The second problem doesn't need you to sum an infinite series and you should think before answering the last one.

Have fun!

Ivalice