It would take 31.5 hours for Dan to complete the same job.
What is work and time relationship?
Work is the effort applied to produce a deliverable or accomplish a task. A certain amount of time (T) is taken to complete a certain work (W).
Work Done = Time Taken × Rate of Work.
Rate of Work = 1 / Time Taken.
Time Taken = 1 / Rate of Work.
According to the question
Dan and Joan were able to clean the attic in 7 hours together
i.e
Rate of Dan = D
Rate of Joan = J
now,
Rate of Work = 1 / Time Taken.
D + J = [tex]\frac{1}{7}[/tex]
It takes Joan 9 hours to complete the same job alone
i.e
J = [tex]\frac{1}{9}[/tex]
Rate of Dan :
D + J = [tex]\frac{1}{7}[/tex]
D + [tex]\frac{1}{9}[/tex] = [tex]\frac{1}{7}[/tex]
D = [tex]\frac{1}{7}[/tex] - [tex]\frac{1}{9}[/tex]
D = [tex]\frac{2}{63}[/tex]
Therefore , Time taken by Dan to complete the same job
As,
Time Taken = 1 / Rate of Work.
Time taken by Dan = [tex]\frac{63}{2}[/tex]
= 31.5 hr
Hence, It would take 31.5 hours for Dan to complete the same job.
To know more about work and time relationship here:
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