Joe packed at a rate of 12/8 cartoons per hour, and Bob packed at a rate of 27/19 cartoon per hour, lets simplify each of this fraction to know if they worked at the same rate
[tex]J=\frac{12}{8}=\frac{6}{4}=\frac{3}{2}[/tex]and for Bob:
[tex]B=\frac{27}{19}[/tex]The fraction cannot be simplified, so they doesn't work at the same rate.