SOLUTION: to a certain job A takes three times as long as B takes. if both of them working together take 9 days, how many days will a take to finish the job working alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: to a certain job A takes three times as long as B takes. if both of them working together take 9 days, how many days will a take to finish the job working alone?      Log On


   

Question 760048: to a certain job A takes three times as long as B takes. if both of them working together take 9 days, how many days will a take to finish the job working alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let A's rate of working = +R%5Ba%5D+
B works 3 times faster, so
B's rate of working = +3R%5Ba%5D+
Their rate working together is ( 1 job ) / ( 9 days )
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If you add their rates of working, you get
their rate working together
+R%5Ba%5D+%2B+3R%5Ba%5D+=+1%2F9+
+4R%5Ba%5D+=+1%2F9+
+R%5Ba%5D+=+1%2F36+
+3R%5Ba%5D+=+3%2F36+
+3R%5Ba%5D+=+1%2F6+
Working alone, A will finish the job in 36 days
check:
+R%5Ba%5D+%2B+3R%5Ba%5D+=+1%2F9+
+1%2F36+%2B+3%2F36+=+1%2F9+
+4%2F36+=+1%2F9+
+1%2F9+=+1%2F9+
OK