How to relate a reaction barrier to the time the reaction needs to proceed?
Here are some back of the envelope numbers from using the Eyring equation:

$$k = \frac{k_{B}T}{h}e^{-\frac{\Delta G^{\ddagger}}{RT}}$$

Let's just assume we're at $298\ \mathrm{K}$ for the reaction, and the reaction is relatively simple:

$$\ce{A-&gt;B}$$

I constructed the following table by plugging in values. $t_{1/2} = \frac{\ln 2}{k}$

\begin{array}{|c|c|}
\hline \Delta G^{\ddagger}\ (\mathrm{kcal\,mol}^{-1})&amp; k\ (\mathrm{s}^{-1}) &amp; t_{1/2} \\ \hline\hline
15 &amp; 63.4 &amp; 10.9\ \mathrm{ms} \\
20 &amp; 0.0138 &amp; 50.2\ \mathrm{s} \\
25 &amp; 2.98\cdot 10^{-6} &amp; 64.6\ \mathrm{h} \\\hline
\end{array}

The values for 15 and 20 $\mathrm{kcal\,mol}^{-1}$ seem pretty consistent with your rule. The top value is a bit off, but we're working with a very small numbers at this point, and there may be other sources of error that we're not accounting for in the model.