Why do farads multiplied by ohms produce a result that has a unit of seconds?
It's the way the units work out. 

Broken down to its form in SI units, a volt is

$$\mathrm{V = \frac{kg \cdot m^2}{A \cdot s^3}}$$

where A is amperes. So, when you divide by current to get ohms, you see that 

$$ \Omega = \mathrm{\frac{kg \cdot m^2}{A^2\cdot s^3}}$$

A farad is:

$$ \mathrm{F=\frac{s^4 \cdot A^2}{m^2 \cdot kg}} $$ 

So when you multiply Ohms by Farads, you're left with seconds:

$$ \Omega \cdot \mathrm{F = \frac{kg \cdot m^2}{A^2\cdot s^3} \cdot \frac{s^4 \cdot A^2}{m^2 \cdot kg} = s} $$