SOLUTION: two old machines and a new one are put to work on a contract. Each of the old ones requires twice as much time as the new one to do the job. Together, the three machines complete t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: two old machines and a new one are put to work on a contract. Each of the old ones requires twice as much time as the new one to do the job. Together, the three machines complete t      Log On


   

Question 697146: two old machines and a new one are put to work on a contract. Each of the old ones requires twice as much time as the new one to do the job. Together, the three machines complete the work in 2 days. How long would it take each machine to do the work alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working to get their
rate working together
Let +r%5B1%5D+ = the rate for an old machine
Let +r%5B2%5D+ = the rate for a new machine
(1) +r%5B1%5D+=+%281%2F2%29%2Ar%5B2%5D+
Note that twice the time means half the rate
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Given: 3 machines working together have
a rate of ( 1 contract ) / ( 2 days )
(2) +r%5B1%5D+%2B+r%5B1%5D+%2B+r%5B2%5D+=+1%2F2+
(2) +2r%5B1%5D+%2B+r%5B2%5D+=+1%2F2+
Substitute (1) into (2)
(2) +2%2A%281%2F2%29%2Ar%5B2%5D+%2B+r%5B2%5D+=+1%2F2+
(2) +r%5B2%5D+%2B+r%5B2%5D+=+1%2F2+
(2) +2r%5B2%5D+=+1%2F2+
(2) +r%5B2%5D+=+1%2F4+
and, since
(1) +r%5B1%5D+=+%281%2F2%29%2Ar%5B2%5D+
(1) +r%5B1%5D+=+%281%2F2%29%2A%281%2F4%29+
(1) +r%5B1%5D+=+1%2F8+
Each old machine takes 8 days to do the work alone
Each new machine takes 4 days to do the work alone
check:
(2) +2r%5B1%5D+%2B+r%5B2%5D+=+1%2F2+
(2) +2%2A%281%2F8%29+%2B+1%2F4+=+1%2F2+
(2) +1%2F4+%2B+1%2F4+=+1%2F2+
(2) +1%2F2+=+1%2F2+
OK