Correct. Let $\displaystyle{t}=\usepackage{cmbright}\Huge\$ Albert's time, in minutes, to eat a platter of hot dogs. Then $\displaystyle{2}{t}=\usepackage{cmbright}\Huge\$ Lester's time to eat a platter of hot dogs. So their rates are $\displaystyle\frac{{1}}{{t}}\usepackage{cmbright}\Huge\$ and $\displaystyle\frac{{1}}{{{2}{t}}}\usepackage{cmbright}\Huge\$ platters per minute.

Here is their combined rate: $\displaystyle\frac{{1}}{{t}}+\frac{{1}}{{{2}{t}}}=\frac{{2}}{{{2}{t}}}+\frac{{1}}{{{2}{t}}}=\frac{{3}}{{{2}{t}}}\usepackage{cmbright}\Huge\$

Therefore: $\displaystyle{\left(\frac{{3}}{{{2}{t}}}\right)}\cdot{10}={1}\usepackage{cmbright}\Huge\$ or $\displaystyle\frac{{30}}{{{2}{t}}}={1}\usepackage{cmbright}\Huge\$ or $\displaystyle\frac{{15}}{{t}}={1}\usepackage{cmbright}\Huge\$

So: $\displaystyle{t}={15}\usepackage{cmbright}\Huge\$ and $\displaystyle{2}{t}={30}\usepackage{cmbright}\Huge\$