If Peggy does it in 12 minutes, she does 1/12 of the work in 1 min
If Butch does it in 27 minutes, he does 1/27 of the work in 1 min
So:
[tex]\begin{gathered} \frac{1}{12}+\frac{1}{27}=\frac{1}{x} \\ \\ \frac{1(27)+1(12)}{27(12)}=\frac{1}{x} \\ \\ \frac{27+12}{324}=\frac{1}{x} \\ \\ \frac{39}{324}=\frac{1}{x} \\ x=\frac{324}{39}=\frac{108}{13} \end{gathered}[/tex]
They can do it in 108/13 or 8.3 minutes working together.
