You may have incorrectly found your rates by using time divided by work. Let $\displaystyle{t}=\usepackage{cmbright}\Huge\$ the time, in hours, it takes the repairman to fix one pair of shoes. Then $\displaystyle{2}{t}=\usepackage{cmbright}\Huge\$ the amount of time it takes the assistant. Their rates are $\displaystyle\frac{{1}}{{t}}\usepackage{cmbright}\Huge\$ and $\displaystyle\frac{{1}}{{{2}{t}}}\usepackage{cmbright}\Huge\$ pairs per hour. Add these rates to get their combined rate. Then use rate times time equals amount of work done.