Correct. Setting up the following system:

$\displaystyle{e}={12.50}\cdot{t}\usepackage{cmbright}\Huge\$

$\displaystyle{484.75}-{e}={10.25}\cdot{\left({44}-{t}\right)}\usepackage{cmbright}\Huge\$

you find that Alex worked for 15 hours, and Chris worked for 29 hours.