SOLUTION: Bea and Yan can do a certain job in 3 hours. On a given day, they worked together for 1 hour then Yan left and Bea finishes the rest of the work in 8 more hours. How long will it t

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Question 982513: Bea and Yan can do a certain job in 3 hours. On a given day, they worked together for 1 hour then Yan left and Bea finishes the rest of the work in 8 more hours. How long will it take for Bea to do the job alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What fraction of the job can they do
working together for 1 hr?
Let +x+ = that fraction
Their rate working together is:
[ 1 job ] / [ 3 hrs ]
---------------------
+1%2F3+=+x%2F1+
+x+=+1%2F3+
That means there is +1+-+1%2F3+=+2%2F3+ of the
job left to do after +1+ hr
---------------------------------
Let +r+ = Bea's rate of working in jobs/hr
+r+=+%28+2%2F3+%29+%2F+8+
+r+=+2%2F24+
+r+=+1%2F12+
This says that Bea can finish 1 job in 12 hrs working alone
check:
+r+=+%28+2%2F3+%29+%2F+8+
+1%2F12+=+%28+2%2F3+%29+%2F+8+
+8%2F12+=+2%2F3+
+2%2F3+=+2%2F3+
OK