Answer
$26^9=5,429,503,678,976$ ms$\approx 172.1$ years
Work Step by Step
9 character password consisting of any 26 characters = $26^9$ possible passwords.
1 millisecond to test each = $26^9=5,429,503,678,976$ milliseconds.
Convert to years:
$\frac{5,429,503,678,976}{1000\cdot 60\cdot 60\cdot 24\cdot 365}\approx 172.1$ years
