Jill and James can clean an attic in 6.24 hours. Had he done it alone, it would have taken James 13 hours. Find how long it would take Jill to do it alone.

Question

Please solve

Answer 1

Has the job been done? Then it will take Jill 0 hours to clean the attic!

If the job has not been done, how is such a precise time, 6.24 hours, known?

 

Leaving aside these philosophic quandries, let's ay the rate of James working alone is 1/13 of the job per hour, i.e. James alone requires 13 hours. Let's also say that Jill's rate, alone, is 1/f of the job per hour (i.e. she fakes f hours, alone).

 

6.24(1/13 + 1/f) = 1 ⇐ time working together is 6.24 hours;left side represents work share of each person; right side is 1 whole job.

 

Solve for f.