Question

at the community savings bank it takes a computer 18 minutes to process and print payroll checks when the second computer is used and the two computers work together the checks can be processed and printed in 14 minutes how long would it take the second computer by itself to process and print the payroll checks

Answer 1

`\begin{gathered} \text{Let }n\text{ be the number of minutes the second computer takes.} \\ \text{With the two computer together, their rate is} \\ (1)/(18)+(1)/(n)=(1)/(14),\text{ get the LCD on the left side} \\ (n+18)/(18n)=(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}}=(252)/(4) \\ n=63 \end{gathered}`

Therefore, the second computer can process and print the payroll checks in 63 minutes.