SOLUTION
Write out the given information
[tex]\begin{gathered} \text{Time for Richard to break up a fight =12 minutes } \\ \text{Time for harold to break up a fight =5 minutes } \end{gathered}[/tex]Let the time at which both of them work be
[tex]R[/tex]Then
The individual rate will be
[tex]\begin{gathered} \text{Richard}=\frac{1}{12} \\ \text{And } \\ \text{Harold}=\frac{1}{5} \end{gathered}[/tex]Then
[tex]\frac{1}{12}+\frac{1}{5}=\frac{1}{R}[/tex]Simplifying fraction, we have
[tex]\begin{gathered} \frac{5+12}{60}=\frac{1}{R} \\ \text{Then} \\ \frac{17}{60}=\frac{1}{R} \end{gathered}[/tex]Hence
[tex]\begin{gathered} R=\frac{60}{17} \\ R=3.53 \end{gathered}[/tex]Therefore
It will take both of them 3.53 minutes to solve it together
