SOLUTION: A roofer requires 14 h to shingle a roof. After the roofer and an apprentice work on a roof for 7 h, the roofer moves on to another job. The apprentice requires 7 more hours to fin

Question 812523: A roofer requires 14 h to shingle a roof. After the roofer and an apprentice work on a roof for 7 h, the roofer moves on to another job. The apprentice requires 7 more hours to finish the job. How long would it take the apprentice, working alone, to do the job?

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
rate = time/job
time = rate * job
job = time/rate
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r = roofer work rate
a = apprentice work rate
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r = 14 hr/job
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use equation:
job = time/rate
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7/(r + a) + 7/a = 1 job
7/(14 + a) + 7/a = 1 job
7a/(a(14 + a)) + 7(14 + a)/(a(14 + a)) = 1 job
7a/(aa + 14a) + 7(14 + a)/(aa + 14a) = 1 job
7a/(aa + 14a) + (7a + 98)/(aa + 14a) = 1 job
(14a + 98)/(aa + 14a) = 1 job
14a + 98 = aa + 14a
14a + 98 = aa + 14a
aa = 98
a = sqrt(98)
a ~= 9.8995 hr/job
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