SOLUTION: Two workers, if they were working together could finish a job in 12 days. If one worker does the first half then the other worker finishes the rest, the job will take them 25 days.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Two workers, if they were working together could finish a job in 12 days. If one worker does the first half then the other worker finishes the rest, the job will take them 25 days.      Log On


   

Question 1077258: Two workers, if they were working together could finish a job in 12 days. If one worker does the first half then the other worker finishes the rest, the job will take them 25 days. How long would it take each worker to do the job by himself.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Times for each worker to do 1 job, x and y.

1%2Fx%2B1%2Fy=1%2F12

Times t and v for each worker to do half a job
t%2Bv=25
-
system%28t%2Fx=1%2F2%2Cv%2Fy=1%2F2%29
system%28t=x%2F2%2Cv=y%2F2%29
-
x%2F2%2By%2F2=25

x%2By=50

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system to solve:
system%281%2Fx%2B1%2Fy=1%2F12%2Cx%2By=50%29
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%28y%2Bx%29%2Fxy=1%2F12
50%2F%28xy%29=1%2F12
xy%2F50=12
xy=12%2A50
xy=600
-
x%2850-x%29=600
-x%5E2%2B50x=600
x%5E2-50x=-600
x%5E2-50x%2B600=0
x=%2850%2B-+sqrt%282500-4%2A600%29%29%2F2
x=%2850%2B-+sqrt%28100%29%29%2F2
x=%2850%2B-+10%29%2F2

system%28x=20%2Cor%2Cx=30%29

Times for each worker alone are 20 days and 30 days.