It would take 6 hours for the assistant to clean the classroom alone.
Step-by-step explanation:
The job in this case is cleaning a classroom.
Paul can clean a classroom in 3 hours
Part of job done by Paul in one hour = 1/3
Similarly, Assistant can clean the same classroom alone but the job this time will take x hours
Part of job done by Paul's assistant = 1/x
Together, Paul and assistant completes the job in 2 hours.
Part of job done by Paul and his assistant together = 1/2
Now, we know that the sum of work done per hour by paul and his assistant separately is equal to the work done by Paul and his assistant together:
Work per hour by Paul + Work per hour by assistant = Work per hour done together
⇒ [tex]\frac{1}{3} +\frac{1}{x} =\frac{1}{2}[/tex]
[tex]\frac{1}{x} =\frac{1}{2} -\frac{1}{3} \\\frac{1}{x} = \frac{3-2}{6} \\\frac{1}{x} =\frac{1}{6}[/tex]
⇒ x = 6 hours
Hence, the assistant would take 6 hours to clean the classroom alone.
Learn more about work done applications from https://brainly.com/question/10694003
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