The average growth of human hair is 0.5 inch per month.
We want to find how long it takes for hair to grow 3 inches.
The growth rate is 0.5 inch/month.
The total growth is 3 inches.
We can set up the equation:
Growth rate $\times$ time = total growth
0.5 inch/month $\times t$ months = 3 inches
$0.5t = 3$
To solve for $t$, we divide both sides of the equation by 0.5:
$t = \frac{3}{0.5} = \frac{3}{\frac{1}{2}} = 3 \times 2 = 6$
So, it takes 6 months for hair to grow 3 inches.
We can also set up a proportion:
$\frac{0.5 \text{ inch}}{1 \text{ month}} = \frac{3 \text{ inches}}{x \text{ months}}$
Cross-multiply:
$0.5x = 3$
$x = \frac{3}{0.5} = 6$
It takes 6 months for hair to grow 3 inches.
Final Answer: The final answer is $\boxed{6}$