You may have incorrectly tried to find rates by dividing time by work, instead of the other way around. The old machine's rate is $\displaystyle\frac{{10}}{{2}}\usepackage{cmbright}\Huge\$ or 5 widgets per hour. The new machine's rate is $\displaystyle\frac{{30}}{{3}}\usepackage{cmbright}\Huge\$ or 10 widgets per hour. Their combined rate equals 75 widgets divided by the time it takes.