SOLUTION: Peter and Paul can do a certaion job in 3 hours. On a given day, they worked together for 1 hour then Paul left and Peter finishes the rest of the work in 8 more hours. How long wi

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Peter and Paul can do a certaion job in 3 hours. On a given day, they worked together for 1 hour then Paul left and Peter finishes the rest of the work in 8 more hours. How long wi      Log On


   

Question 745788: Peter and Paul can do a certaion job in 3 hours. On a given day, they worked together for 1 hour then Paul left and Peter finishes the rest of the work in 8 more hours. How long will it take Peter to do the job alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If they can do the whole job in 3 hrs working
together, then in 1 hour, they can do +1%2F3+
of the job
That means there is 2/3 of the job left to do
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Then, ( Peter's rate of working ) x ( 8 hrs ) = 2/3
Let +R%5B1%5D+ = Peter's rate of working
+8R%5B1%5D+=+2%2F3+
+R%5B1%5D+=+2%2F24+
+R%5B1%5D+=+1%2F12+
Peter would take 12 hrs to do the job alone
check:
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Let +R%5B2%5D+ = Paul's rate of working
+R%5B1%5D+%2B+R%5B2%5D+=+1%2F3+
+1%2F12+%2B+R%5B2%5D+=+1%2F3+
+R%5B2%5D+=+4%2F12+-+1%2F12+
+R%5B2%5D+=+1%2F4+
In +1+ hr,
+1%2F12+%2B+3%2F12+=+x%2F1+
+x+=+1%2F3+
So, +2%2F3+ of the job is left
Peter does
+1%2F12++=+%282%2F3%29+%2F+8+
+1%2F12+=+1%2F12+
OK