One of the follow-on letters from here
suggested you could work out the diameter of the universe by multiplying the time since the Big Bang by the speed of light.
Alas, as I understand it the theory is that space-time itself expanded, rather than just stuff inside space-time. The expansion of space-time is not, as far as I am aware, limited to the speed of light.
This hypothesis explains why stars (at least those that are furthest away from us) are all moving away from us, and also why the cosmic background radiation seems pretty uniform rather than all coming from one direction - the afterglow of the big bang is all around us.