SOLUTION: One group of workers can do a job in 8 days. After this group has worked 3 days, another group joins it and together they complete the job in 3 more days. In what time could the se

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: One group of workers can do a job in 8 days. After this group has worked 3 days, another group joins it and together they complete the job in 3 more days. In what time could the se      Log On


   

Question 667143: One group of workers can do a job in 8 days. After this group has worked 3 days, another group joins it and together they complete the job in 3 more days. In what time could the second group have done the job alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the 1st group can do 1 job in 8 days,
they do 1/8 of the job in 1 day
So, in 3 days they do 3/8 of the job
That means 5/8 of the job is left to be done
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Let +d+ = the number of days the 2nd
group takes to do the job alone.
Add their rates of working to get the rate
at which they can do the 5/8 of a job working together
+1%2F8+%2B+1%2Fd+=+%285%2F8%29%2F3+
+1%2F8+%2B+1%2Fd+=+5%2F24+
Multiply both sides by +24d+
+3d+%2B+24+=+5d+
+2d+=+24+
+d+=+12+
The 2nd group could have done the job alone in 12 days