= Solution
Set the spatial-curvature constant to zero in the stipulated matter-only <Friedmann equation> to get $\rho_c=3H^2/(8\pi G)$. Conservation of <pressureless matter> with $R(t_0)=1$ gives $\rho=\rho_0/R^3$, and therefore
$$
\dot R^2=\frac{8\pi G\rho_0}{3R},\qquad R^{3/2}=\frac32\sqrt{\frac{8\pi G\rho_0}{3}}\,t.
$$
Choosing the <Big Bang> as $t=0$ yields $R=(t/t_0)^{2/3}$ and $H=2/(3t)$. Consequently $\boxed{t_0=2/(3H_0)\simeq9.3\ \mathrm{Gyr}}$ for the supplied $H_0$. This is the age of the flat pressureless model without a <cosmological constant>, not a determination in the current multi-component cosmological model.
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