let

x = the minutes Joan needs to file the reports by herself, x>0

1/x reports per min is the rate of Joan

y = the minutes Jane needs to file the reports by herself, y>0

1/y reports per min is the rate of Jane

It takes Joan 5 times longer than Jane to file the reports:

x = 5y

Together they can file the reports in 35 minutes thus their together rate is 1/35 reports per min:

1/x + 1/y = 1/35

plug x = 5y into the last equation:

1/(5y) + 1/y = 1/35

by solving we find

y = 42 min

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x = 5*42

x = 210 min

Joan needs 210 min to file the reports by herself.

Joan needs 42 min to file the reports by herself.