age of universe

[b_o3]

Assume that the current age of the universe is 13.4 billion years old, and that we live in a matter-dominated, omega_m = 1, critical universe, what is the age of the universe at redshift 0.6? HINT: use the current age of the universe to pin down the proportionality relationship between age and the scale factor

 

I know that (t_o) proportional to (1/H_o) proportional to (1/z), but I don't know how to connect this with the scale factor...and I have no idea how to "use the current age of the universe to pin down the proportionality relationship between age and the scale factor"