SOLUTION: i have solved that if Worker A finishes a job in 8 days and worker B finishes it in 12 days they complete 5/24 of the job in 1 day. I also solved that they complete 5/8 of the job

Algebra ->  Rate-of-work-word-problems -> SOLUTION: i have solved that if Worker A finishes a job in 8 days and worker B finishes it in 12 days they complete 5/24 of the job in 1 day. I also solved that they complete 5/8 of the job       Log On


   

Question 560352: i have solved that if Worker A finishes a job in 8 days and worker B finishes it in 12 days they complete 5/24 of the job in 1 day. I also solved that they complete 5/8 of the job in 3 days. I think that i am stuck on how many days it will take the 2 workers to finish the job. I believe it is 5/8x = 1 which is 1 3/5 days. I am stumped on the question: If B worked alone for 3 days how many days will it take A alone to finish the remaining work? Can you help please.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
just use the same ratio
+%285%2F8%29+%2F+3+ job/days
Multiply top and bottom by +8%2F5+
+1+%2F+%28%288%2F5%29%2A3%29+
+1+%2F+%2824%2F5%29+
This is 1 job completed in 4 and 4/5 days
This makes sense, because it will take a little longer
than 3 days if 5/8 of the job is done in 3 days
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How much of the job can B get done in 3 days?
B's rate = +1%2F12+ job/days. This is the same as
+%281%2F12%29+%2F+1+ job/days
In 3 days B will get 3 times as much done, or
+3%2F12+=+1%2F4+ job
Now A has to do +3%2F4+ of the job to finish it
A's rate = +1%2F8+ job/days
Note that ( days ) = ( job ) / ( job/days ) )
+%28+3%2F4%29+%2F+%28+1%2F8+%29+=+24%2F4+
+24%2F4+=+6+
It will take A 6 days to finish the job alone