Q&A: Cosmology

Q:
When I read about the estimate of the age of the universe I see a paradox. Reports on NASA's site estimate telescopes like the HST can see about 10 billion light years and the latest speed of the expansion of the universe is about 300 kps. For the universe to be 10 billion light years + in diameter it would take 10 trillion years to be that size at that speed. Am I misunderstanding something?

A:
The universe is not expanding at a uniform rate, but for a rough estimate we can assume that the most distant galaxies are rushing away from us at the speed of light. There are about 30 million seconds in a year, so at 300,000 km/sec the universe would expand by an amount (30,000,000 sec) X 300,000 km/sec = 9,000,000,000,000 km = 9 trillion km = 1 light year. So in 10 billion years the universe would expand to about 10 billion light years.