Answer: The apprentice work for 54 hours alone to do the job.
Step-by-step explanation:
Since we have given that
Number of hours a roofer requires = 9 hours
Number of hours the roofer and an apprentice work on a roof = 6 hours
Number of hours the apprentice requires more = 12 hours
Let x be the time taken by the apprentice alone.
According to question, we get that
[tex]\dfrac{6}{9}+\dfrac{18}{x}=1\\\\\dfrac{2}{3}+\dfrac{18}{x}=1\\\\\dfrac{18}{x}=1-\dfrac{2}{3}\\\\\dfrac{18}{x}=\dfrac{1}{3}\\\\x=18\times 3\\\\x=54\ hours[/tex]
Hence, the apprentice work for 54 hours alone to do the job.
