How can I use Hubble's Law to find the age of the Universe?

Question

I'm so confused. I understand Hubble's Law (for the most part), but I'm not quite sure how I would use it to discover the age of the Universe?? How do we know that the Constant is 70 km/sec/mpc instead of something smaller? because if it was smaller, the Universe would be older, right? and if it was larger the Universe would be younger? How do I calculate the correct age?

Answer 1

Supposedly we just take the reciprocal...

Answer 2

H = 70 km/(sec*Mpc)

The Hubble time is 1/H as km and Mpc=3.09 × 10^19 km are both units of length. Assume the rate of expansion was constant, this time is the age of the Universe. Working it out, I get 1/H = 4.35×10^17 s or 13.8 billion years.