# What is the calculation of the Hubble time based on? [duplicate]

I understand that Hubble's law states that:$\\$

$v=H_{0}D$

However, given that the Hubble time (an estimate of the age of the universe) is given by $\frac{1}{H_{0}}$, doesn't that mean...

$v=H_{0}D\quad \to \quad \frac{D}{v}=\frac{1}{H_{0}}$

Now, if we are saying that $t_{H}=\frac{1}{H_{0}}$, it's equivalent to saying that $t_{H}=\frac{D}{v}$; so wouldn't this mean that we are implying that the recessional velocity of all objects in the universe has been constant from the beginning of time?

Since D is increasing at a rate $v$ at any time, then $H_{0}D$ must also be increasing; then this would mean that $v$ isn't constant.

Based on the above argument, what is a better way to interpret the Hubble time?