SOLUTION: A can do as much work in 5 days as B can do in 6 days.If both of them work together can do the work in 12 days,in how many days can each of them complete the work alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A can do as much work in 5 days as B can do in 6 days.If both of them work together can do the work in 12 days,in how many days can each of them complete the work alone?      Log On


   



Question 1062647: A can do as much work in 5 days as B can do in 6 days.If both of them work together can do the work in 12 days,in how many days can each of them complete the work alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R%5Ba%5D+ = A's rate of working
Let +R%5Bb%5D+ = B's rate of working
+R%5Ba%5D+%2F+R%5Bb%5D+=+6%2F5+ ( A works faster than B )
+5R%5Ba%5D+=+6R%5Bb%5D+
+R%5Bb%5D+=+%28+5%2F6+%29%2AR%5Ba%5D+
-------------------------
Working together, their rate is +1%2F12+
which is [ 1 job done ] / [ 12 days ]
+R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F12+
+R%5Ba%5D+%2B+%285%2F6%29%2AR%5Ba%5D+=+1%2F12+
+R%5Ba%5D+=+%28+6%2F11+%29%2A%28+1%2F12+%29+
+R%5Ba%5D+=+1%2F22+
and
+R%5Bb%5D+=+%28+5%2F6+%29%2AR%5Ba%5D+
+R%5Bb%5D+=+%28+5%2F6+%29%2A%281%2F22%29+
+R%5Bb%5D+=+5%2F132+
+R%5Bb%5D+=+1%2F26.4+
----------------------------
A can do the job in 22 days
B can do the job in 26.4 days
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check:
+1%2F22+%2B+1%2F26.4+=+1%2F12+
+.04545+%2B+.037878+=+.08333+
+.083328+=+.08333+
close enough
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