[tex]\begin{gathered} \text{Let }n\text{ be the number of minutes the second computer takes.} \\ \text{With the two computer together, their rate is} \\ \frac{1}{18}+\frac{1}{n}=\frac{1}{14},\text{ get the LCD on the left side} \\ \frac{n+18}{18n}=\frac{1}{14},\text{ next cross multiply both the left and right side} \\ (18n)(1)=(14)(n+18),\text{ simplify} \\ 18n=14\cdot n+252 \\ 18n=14n+252,\text{ bring subtract both sides by }14n \\ 18n-14n=14n-14n+252 \\ 4n=252,\text{ divide both sides by 4} \\ \frac{\cancel{4}n}{\cancel{4}}=\frac{252}{4} \\ n=63 \end{gathered}[/tex]
Therefore, the second computer can process and print the payroll checks in 63 minutes.
