SOLUTION: jun and mike working together complete a job for 6 days, or they complete the job if jun works for 12 days and mike works for 3 days. how long would it take each man,alone to compl

Algebra ->  Rate-of-work-word-problems -> SOLUTION: jun and mike working together complete a job for 6 days, or they complete the job if jun works for 12 days and mike works for 3 days. how long would it take each man,alone to compl      Log On


   

Question 782048: jun and mike working together complete a job for 6 days, or they complete the job if jun works for 12 days and mike works for 3 days. how long would it take each man,alone to complete the job?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R%5Bj%5D+ = jun's rate of working
Let +R%5Bm%5D+ = Mike's rate of working
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(1) +R%5Bj%5D+%2B+R%5Bm%5D+=+1%2F6+
(2) +12R%5Bj%5D+%2B+3R%5Bm%5D+=+1+
( note that +1%2F6+ is ( 1 job ) / ( 6 days )
and +1+ is 1 job )
--------------------------------
(1) +6R%5Bj%5D+%2B+6R%5Bm%5D+=+1+
(2) +12R%5Bj%5D+%2B+3R%5Bm%5D+=+1+
Multiply both sides of (2) by +2+
and subtract (1) from (2)
(2) +24R%5Bj%5D+%2B+6R%5Bm%5D+=+2+
(1) +-6R%5Bj%5D+-+6R%5Bm%5D+=+-1+
+18R%5Bj%5D+=+1+
+R%5Bj%5D+=+1%2F18+
-------------------
and, since
(1) +R%5Bj%5D+%2B+R%5Bm%5D+=+1%2F6+
(1) +1%2F18+%2B+R%5Bm%5D+=+3%2F18+
(1) +R%5Bm%5D+=+3%2F18+-+1%2F18+
(1) +R%5Bm%5D+=+2%2F18+
(1) +R%5Bm%5D+=+1%2F9+
----------------------
Working alone, Jun can do the job in 18 days
Working alone, Mike can do the job in 9 days
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check:
(2) +12R%5Bj%5D+%2B+3R%5Bm%5D+=+1+
(2) +12%2A%281%2F18%29+%2B+3%2A%281%2F9%29+=+1+
(2) +2%2F3+%2B+1%2F3+=+1+
OK