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Working alone,Maria can complete a task in 100 minutes.Ann can complete the same job in 2 hours.They work together for 30 minutes when Liu,the new employee,joins and begin helping.They finish the job 20 minutes later.How long will it take Liu to complete the same job alone?

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Check my work, before you hand it in -- there could be some DELIBERATE errors in my fractions. :-)

Marie takes 100 minutes for 1 job.
Marie took 50 minutes for 1/2 job.

Ann takes 120 minutes for 1 job.
Ann took 30 minutes and did 1/4 job.
Ann took 20 more minutes and did 1/6 job.

Together Marie & Ann did 1/2 plus 1/4 plus 1/6 job in 50 minutes.
Together Marie & Ann did 6/12 plus 3/12 plus 2/12 job in 50 minutes.
Together Marie & Ann did 11/12 job in 50 minutes.

Liu did the rest (1-(1/2+1/4+1/6)) job in 20 minutes.
Liu did the rest (1-(4+3+2)/12) job in 20 minutes.
Liu did the rest (1-9/12) in 20 minutes.
Liu did the rest (1/4) in 20 minutes.
Liu worked for 5 minutes.

Posted on Sep 17, 2010

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