<PRE><B>Question 508414</B>
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


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