# SOLUTION: A roofer and his assistant working together can finish a roofing job in 4 hours. The roofer working alone could finish the job in 6 hours less than the assistant working alone. How

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A roofer and his assistant working together can finish a roofing job in 4 hours. The roofer working alone could finish the job in 6 hours less than the assistant working alone. How      Log On

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 Question 508414: A roofer and his assistant working together can finish a roofing job in 4 hours. The roofer working alone could finish the job in 6 hours less than the assistant working alone. How long would it take the roofer working alone? Answer by nerdybill(7090)   (Show Source): You can put this solution on YOUR website!A roofer and his assistant working together can finish a roofing job in 4 hours. The roofer working alone could finish the job in 6 hours less than the assistant working alone. How long would it take the roofer working alone? . Let x = time (hours) for assistant alone then x-6 = time (hours) for roofer . 4(1/x + 1/(x-6)) = 1 multiplying both sides by x(x-6): 4((x-6) + x) = x(x-6) 4(2x-6) = x^2-6x 8x-24 = x^2-6x -24 = x^2-14x 0 = x^2-14x+24 0 = (x-2)(x-12) x = {2,12} we can throw out the 2 (extraneous) leaving: x = 12 hours (assistant) . Roofer working alone: x-6 = 12-6 = 6 hours