Age of Universe, Redshift & Scale Factor

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Homework Statement


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


Homework Equations


Some formulas that I have found are:
1+z=R(t_o)/R(t) (redshift and scale factor)
H_o= cz/d (hubble constant)
omega_m=1 means k=0 and matter-dominated together with k=0 critical universe implies that the age of the universe t_o = 2/(3H_o)
For k=0 critical universe R(t) is proportional to t^(2/3)

The Attempt at a Solution


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"


Can someone please help me out? I did all the reading but was still unable to solve this problem, no matter how hard I tried...

Thanks for helping!
 
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