SOLUTION: A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

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Question 770912: A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R%5Bb%5D+ = B's rate of working
+1.3%2AR%5Bb%5D+ = A's rate of working
---------------
Also given is:
A's rate of working is ( 1 job ) / ( 23 days )
+1.3%2AR%5Bb%5D+=+1%2F23+
+R%5Bb%5D+=+1%2F29.9+
and
+R%5Ba%5D+=+1%2F23+
----------------
Let +t+ = time in days to finish
job working together
+R%5Ba%5D+%2B+r%5Bb%5D+=+1%2Ft+
+1%2F23+%2B+1%2F29.9+=+1%2Ft+
Multiply both sides by +23%2A29.9%2At+
+29.9t+%2B+23t+=+23%2A29.9+
+52.9t+=+687.7+
+t+=+13+
Working together, they can do the
job in 13 days
check:
+1%2F23+%2B+1%2F29.9+=+1%2F13+
+.04348+%2B+.03344+=+.07692+
+.07692+=+.07692+
OK