As teachers, we want to encourage our students to ask searching questions on topics like how old the Universe is, how much of the Universe we can actually see and how far away the cosmic microwave background radiation is. But how many of us can honestly say we know the answers? And, even if we know the answers, how are we going to respond to the student's next obvious question regarding how the cosmic microwave background radiation can be 90 billion light years away when the Universe is only 13.6 billion years old? In this article, using some straightforward mathematics I derive some interesting formulae which will not only provide reasonably accurate numerical answers, but, more importantly, give much needed insight into the paradoxes which abound when applying general relativity to the Universe as a whole. (Contains 3 figures.)