SOLUTION: A roofer requires 12 hours to shingle a roof, working alone. After the roofer and his assistant work on a roof for 3 hours, the roofer goes off to have a beer and never returns. th

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A roofer requires 12 hours to shingle a roof, working alone. After the roofer and his assistant work on a roof for 3 hours, the roofer goes off to have a beer and never returns. th      Log On


   

Question 863598: A roofer requires 12 hours to shingle a roof, working alone. After the roofer and his assistant work on a roof for 3 hours, the roofer goes off to have a beer and never returns. the assistant continues to work after the roofer leaves and it requires him 12 more hours to complete the job. How long would it take for the assistant, working alone, to do the whole job?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Roofer rate, 1/12 jobs per hour
Assistant's rate, 1/u jobs per hour

Equation for the description:
Using R*T=J rate time job,
%281%2F12%2B1%2Fu%29%2A3%2B%281%2Fu%29%2A12=1
That is the sum of the two work situations. One expression for both working together three hours, and the other for just the assistant working alone for 12 hours.

Solve for u.
3%2F12%2B3%2Fu%2B12%2Fu=1
1%2F4%2B15%2Fu=1
.
u%2B60=4u
60=3u
highlight%28u=20%29 hours for the assistant if doing 1 job alone.