Theoretical Astronomy Question.
 

Okay, so if there are asteroids in the same orbit as Earth. Must they be travelling at the same speed as Earth or not?

see: Trojan asteroid discovered in Earth orbit
http://www.abc.net.au/news/2011-07-2...-orbit/2814204

If an asteroid on the opposite side of the Sun in Earth's orbit is travelling either a little faster or a little slower than one would expect the Earth either to catchup at some point in time or the asteroid to catchup to Earth, yes?

Question: If the Earth is travelling at 29.8 kilometers per second and the asteroid exactly opposite the Earth is travelling at say 29.6 kilometers per second. How long before the Earth would catch up to it and collide with it?

74 years, excluding gravitational effects.