SOLUTION: How do I plug this problem into My calculator so I can solve? Jane wants to buy a photocopier. The salesman has the following information on 3 models. If all 3 are used, a speci

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Question 1109172: How do I plug this problem into My calculator so I can solve?
Jane wants to buy a photocopier. The salesman has the following information on 3 models. If all 3 are used, a specific job can be done in 50 minutes. If copier A operates for 20 minutes and copier B for 50 minutes, one-half the job is finished. If copier B operates for 30 minutes and copier C for 80 minutes, three-fifths of the job is done. Which is the fastest copier, and how long does it take for this copier to finish the whole job?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the rate, +R+ = [ jobs done ] / [ time in min ]
Let the rates of the 3 copiers = +R%5Ba%5D+, +R%5Bb%5D+, +R%5Bc%5D+
You can add the rates to get their rate working together.
Also: +R+ x time working = fraction of the job completed.
(1) +R%5Ba%5D+%2B+R%5Bb%5D+%2B+R%5Bc%5D+=+1%2F50+
(2) +R%5Ba%5D%2A20+%2B+R%5Bb%5D%2A50+=+1%2F2+
(3) +R%5Bb%5D%2A30+%2B+R%5Bc%5D%2A80+=+3%2F5+
----------------------------------
(2) +20%2AR%5Ba%5D+=+-50%2AR%5Bb%5D+%2B+1%2F2+
(3) +80%2AR%5Bc%5D+=+-30%2AR%5Bb%5D+%2B+3%2F5+
----------------------------------
(2) +R%5Ba%5D+=+-%2850%2F20%29%2AR%5Bb%5D+%2B+1%2F40+
(3) +R%5Bc%5D+=+-%2830%2F80%29%2AR%5Bb%5D+%2B+3%2F400+
-----------------------------------
(1)
(1) +-%2820%2F8%29%2AR%5Bb%5D+%2B+13%2F400+%2B+R%5Bb%5D+-+%283%2F8%29%2AR%5Bb%5D+=+8%2F400+
(1) +%288%2F8%29%2AR%5Bb%5D+-+%2823%2F8%29%2AR%5Bb%5D+=+-5%2F400+
(1) +-%2815%2F8%29%2AR%5Bb%5D+=+-5%2F400+
(1) +R%5Bb%5D+=+%28+8%2F15+%29%2A%28+5%2F400+%29+
(1) +R%5Bb%5D+=+%28+1%2F15+%29%2A%28+5%2F50+%29+
(1) +R%5Bb%5D+=+1%2F150+
-----------------------------------
(2) +R%5Ba%5D+=+-%2850%2F20%29%2AR%5Bb%5D+%2B+1%2F40+
(2) +R%5Ba%5D+=+-%285%2F2%29%2A%281%2F150%29+%2B+1.40+
(2) +R%5Ba%5D+=+-1%2F60+%2B+1%2F40+
(2) +R%5Ba%5D+=+-2%2F120+%2B+3%2F120+
(2) +R%5Ba%5D+=+1%2F120+
------------------------------------
(3) +R%5Bc%5D+=+-%2830%2F80%29%2AR%5Bb%5D+%2B+3%2F400+
(3) +R%5Bc%5D+=+-%283%2F8%29%2AR%5Bb%5D+%2B+3%2F400+
(3) +R%5Bc%5D+=+-%283%2F8%29%2A%281%2F150%29+%2B+3%2F400+
(3) +R%5Bc%5D+=+-3%2F1200+%2B+3%2F400+
(3) +R%5Bc%5D+=+-1%2F400+%2B+3%2F400+
(3) +R%5Bc%5D+=+1%2F200+
------------------------------------
The fastest rate is copier A which is
1 job / 120 min
------------------------------------
check answer:
(1) +R%5Ba%5D+%2B+R%5Bb%5D+%2B+R%5Bc%5D+=+1%2F50+
(1) +1%2F120+%2B+1%2F150+%2B+1%2F200+=+1%2F50+
(1) +5%2F600+%2B+4%2F600+%2B+3%2F600+=+12%2F600+
(1) +12%2F600+=+12%2F600+
OK
You can check (2) and (3)
Find a way to plug the numbers into the calculator, I guess.
Check my math & get 2nd opinion if needed




Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
This problem is exactly Problem 7 of the lesson
    - Joint-work problems for 3 participants
in this site. See the solution there.

The request regarding calculators seems to be strange.

The problem is/was designed for solution through algebra and logical reasoning and does no assume using calculators.