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working alone, maria can complete a task in 100 minutes. shaniqua can complete the same task in 2 hours. they work together for 30 minutes when liu, the new employee, joins and begins helping. they finish the task 20 minutes later, how long would it take liu, to complete the task alone?

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Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
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Maria does 1/100 or a workload in a minute, Shaniqua does 1/120 of a workload in a minute (since there are 120 minutes in 2 hours). Together they do (1/100+1/120)=11/600 in a minute.
In 30 minutes they would finish 11/20 of the whole workload. The remaining work load is 9/20 of the whole workload. When Liu joins in, they finish in 20 minutes, that is they do 9/400 of workload in a minute.
The speed of Liu is then 9/400-11/600=5/1200=1/240; It means that she does 1/240 of a workload in a minute. Thus, she will finish the task alone in 240 minutes or 4 hours.