The rate of completed problems can be calculated using the equation:
[tex]r=\frac{\#\text{ of problems}}{t}[/tex]Then, for Adrian and Abbi:
[tex]\begin{gathered} r_{\text{Adrian}}=\frac{14}{1.2h}=\frac{35}{3}\text{ problems per hour} \\ r_{\text{Abbi}}=\frac{11}{0.5h}=22\text{ problems per hour} \end{gathered}[/tex]If they work together, the total rate will be the sum of the individual rates:
[tex]r_{\text{Total}}=\frac{35}{3}+22=\frac{101}{3}\text{ problems per hour}[/tex]We know the rate and the number of problems (32), so using the equation for the rate:
[tex]\begin{gathered} \frac{101}{3}=\frac{32}{t} \\ t=32\cdot\frac{3}{101} \\ t=\frac{96}{101}\text{ hours }\approx0.95\text{ hours} \end{gathered}[/tex]