You may have incorrectly tried to find rates by dividing time by work, instead of the other way around. The first potter's rate is $\displaystyle\frac{{15}}{{5}}\usepackage{cmbright}\Huge\$ or 3 mugs per hour. The second potter's rate is $\displaystyle\frac{{12}}{{3}}\usepackage{cmbright}\Huge\$ or 4 mugs per hour. Their combined rate equals 63 mugs divided by the time it takes. The correct answer is 9 hours.