Age of the Universe: Solve for t_0

[NeedPhysHelp8]

Hi all,
Hoping you can help with this problem!

Homework Statement

For a flat universe, show that $$t_{0}=2/3 (H_{0})^{-1}$$ ? Seems like a simple problem I just don't really know where to start.

Homework Equations

Hubble's law $$v= H_{0}r$$
and then $$t= 1/H_{0}$$

The Attempt at a Solution

I just need guidance where to start. Flat universe means that expansion is constant in any direction right? What do I do?

 

[mgb_phys]

flat universe means the Hubble constant is constant.

Then 1/hubble constant has units time.
Think of the equations for something that doubles/halves with a constant time interval

 

[NeedPhysHelp8]

How about the kinematic equation: x(t)= vt + 1/2at^2
Not sure if this is right and what to do with it? maybe take a derivatives of both sides?

 

[NeedPhysHelp8]

I still can't figure out the answer, can someone give me a hint please