SOLUTION: A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B dad to leave and A alone completed the remaining work. The

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Question 770917: A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B dad to leave and A alone completed the remaining work. The whole work was completed in_____.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A's rate of working:
( 1 job ) / ( 15 days )
B's rate of working:
{ 1 job ) / ( 10 days )
-----------------
What fraction of the job did they get
done in 2 days? Let the fraction = k
+1%2F15+%2B+1%2F10+=+k%2F2+
Multiply both sides by +30+
+2+%2B+3+=+15k+
+k+=+5%2F15+
+k+=+1%2F3+
That means there is 2/3 of the job left to finish
---------------
A working alone:
Let +t+ = time in days to finish job
+1%2F15+=+%28+2%2F3%29+%2F+t+
+t%2A%28+1%2F15+%29+=+2%2F3+
+t+=+15%2A%28+2%2F3+%29+
+t+=+10+ days
---------------
The whole work was completed in +2+%2B+10+=+12+ days