Micah is planning a road trip. He estimates that he will drive a total of of $\displaystyle{9}\frac{{3}}{{4}}\usepackage{cmbright}\Huge\$ hours. He wants to stop for gas after $\displaystyle\frac{{1}}{{3}}\usepackage{cmbright}\Huge\$ of the total time has passed. How long will he drive before he stops for gas? Express your answer as a mixed number.