A roofer requires 9 h to a shingle roof. After the roofer and an apprentice work on a roof for 6 h, the roofer moves on to another job. The apprentice requires 12 more hours to finish the job. How long would it take the apprentice, working alone, to do the job?
Accepted Solution
A:
Answer: The apprentice work for 54 hours alone to do the job.Step-by-step explanation:Since we have given thatNumber of hours a roofer requires = 9 hoursNumber of hours the roofer and an apprentice work on a roof = 6 hoursNumber of hours the apprentice requires more = 12 hoursLet 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.