Question

It takes Joan 6 times longer than Jane to file the reports. Together they can file the reports in 42 minutes. How long would it take each woman to file the reports by herself?

Answer 1

Let x be the number of minutes that Jane can do the job alone. With this representation, Joan will take 6x minutes to do the job. The equation that relates their rates of doing the work and time is,
                   (1/x + 1/6x)(42) = 1
The value of x is 49 minutes. Therefore, Jane can do it in 49 minutes and Joan can do it in 249 minutes or 4.9 hours.