E O, this is how I sorted it out for myself when I was struggling with this sort of thing. Hope it helps. You may think of a clever way round the relative speed limit of a little under 300,000 kps. Suppose you had access to an enormously long space craft that was capable of travelling at ninety percent of the speed of light. Inside this, you have a small craft which is capable of twenty percent of light speed. Surely, all you need to do is fly both of these craft, one within the other, at their maximum speeds and you will be exceeding the speed of light relative to the Earth. It seems logical, but what we have to remember is that although the speed we are using for the big craft is its speed relative to the Earth, the speed of the small craft is its speed relative to the big craft. Does this make any difference? If I am on a train travelling at sixty miles per hour, and I run, in the same direction at ten miles per hour, then my speed relative to the track must be seventy miles per hour. So why would the same reasoning not work for space craft? The truth is that the same reasoning does work for both; it is the earthbound example that is wrong, but because the speeds involved are so small in comparison to the speed of light, the straightforward addition we used is so close it makes no real difference. We have no instruments capable of detecting so small a difference. However, when we are dealing with speeds that are appreciable fractions of the speed of light, the difference becomes significant and we have to use the relativistic velocity addition formula. The formula is expressed in the following equation:

v_{1}+ v_{2}

v' = ----------------------------------------

1 + (v_{1}+v_{2})

In this equation the symbol v' (v prime) is the speed of the small craft relative to the Earth.

V_{1} is the speed of the big craft relative to the Earth. (90%c)

V_{2} is the speed of the small craft relative to the big craft. (20%c)

All speeds are expressed as fractions of the speed of light, so inserting the relevant values into the above equation, (which I'm not going to do because I had enough trouble with the other one) gives us: 0.93 or 93% of the speed of light.