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Intern
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Work [#permalink] New post 07 Aug 2008, 18:30
Could someone help me on this work question:

6 machines each working at the same constant rate together can complete a job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?
The answer is 3 but I don't understand how it was derived.
Thanks folks
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Re: Work [#permalink] New post 07 Aug 2008, 18:38
6 * (1/x ) = 1/12
x = 72

r = 1/72

(6+y)* (1/72) = 1/8
y = 3
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Re: Work [#permalink] New post 07 Aug 2008, 18:40
6 machines can do the work in 12 days, that means 1 machine does 1/(6*12) th of the task in a day.
so, to do the work in 1 day, we will need 6*12 machines ; to do the work in 8 days, it will need (6*12)/8 machines i.e. 9 machines. so additional 3 machines
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Re: Work [#permalink] New post 07 Aug 2008, 18:41
pattydread wrote:
Could someone help me on this work question:

6 machines each working at the same constant rate together can complete a job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?
The answer is 3 but I don't understand how it was derived.
Thanks folks


6x12 = 8 x n
n = 9.

additional = 9-6 = 3 workers
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Re: Work [#permalink] New post 07 Aug 2008, 18:44
pattydread wrote:
Could someone help me on this work question:

6 machines each working at the same constant rate together can complete a job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?
The answer is 3 but I don't understand how it was derived.
Thanks folks


I crack such qs this way--You need to understand the logic behind the working though.

6 macs, 1 job, 12 days -----> 1 day, 6 macs, 1/12th of the job OR mathematically, 6m==1/12 (where m is the rate of job completion each machine)

6m=1/12
m=1/(12*6) (Remember, in the denominator, 12 represents the job completion days and 6 represents the number of machines) --> (i)

m=1/72 (that is, each machine can complete 1/72th of the job every day; it is the rate of a machine)

Now, break up the denominator to have job completion days and number of machines. refer (i) for the format

m=1/72=1/(8*9)

Why 8*9? we need 8 in place of 12 i.e. we need some n number of machines to work for us and complete the same job in 8 days instead of 12 days. We can afford to have such a break up because the machines are still the same: rates won't change.

so, 8 represents the number of days and 9 represents the number of machines.

9m=1/8 OR verbally, 9 machines are required to complete a job in 8 days.

Hope this helps! :)
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Re: Work [#permalink] New post 07 Aug 2008, 20:08
The responses were really helpful. Thanks alot
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Re: Work [#permalink] New post 09 Aug 2008, 13:37
6 machine complete a job in 12 days
1 machine complete a job in 72 days
To complete a job in 8 days you need 72/8= 9 machines
So you need 9-6=3 more machines
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Re: Work   [#permalink] 09 Aug 2008, 13:37
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