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Six machines, all working at the same steady rate, can

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Six machines, all working at the same steady rate, can [#permalink] New post 22 Apr 2005, 09:40
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Six machines, all working at the same steady rate, can finish a particular job in 1 hour. If we wanted to finish the same job in 40 minutes, how many identical machines would we have to add?

A. 1
B. 2
C. 3
D. 6
E. 9
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 [#permalink] New post 22 Apr 2005, 09:55
6 Machines take 60 mins.
therefore the number of machines needed to finish the job in 40 mins =

(60/40)*6=9 machines.

number of extra machines required=9-6=3.
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 [#permalink] New post 22 Apr 2005, 12:31
More formal solution

J - job
M - average rate of a single machine

J/(6 * M) = 1
J/((6+x) * M) = 2/3

J = 6M * 1

6M * 1 / ((6+x) * M) = 2/3

6 / (6+x) = 2/3

2 * (6+x) = 18

x = 3
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 [#permalink] New post 24 Apr 2005, 09:20
60 mins job requires = 6 machines
1 min job would require = 60*6 machines ( as number of m/c would be more)
40 min job would require = 60*6/40 = 9 m/c

No of machines required = 9-6 =3
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 [#permalink] New post 24 Apr 2005, 19:42
Agree with 3

6 machines during 1h -> 6h -> 360mn

x*40 = 360
x = 9

9-6 = 3 :wink:
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 [#permalink] New post 25 Apr 2005, 05:48
add 3.

agree with the above-mentioned workings. :-D
  [#permalink] 25 Apr 2005, 05:48
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