Six machines, each working at the same constant rate, together can complete a certain 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?
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machines work problem (i never get these right)
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If 6 machines take 12 days to complete the job, then we can say that the job takes 72 "machine days" to complete the job (6x12=72)josh80 wrote:Six machines, each working at the same constant rate, together can complete a certain 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?
A) 2
B) 3
C) 4
D) 6
E) 8
To complete the job in 8 days would require 9 machines (72 machine days divided by 8 day = 9 machines)
So, we need an additional 3 machines.
Answer = B
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Approach 1:josh80 wrote:Six machines, each working at the same constant rate, together can complete a certain 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?
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Since Work done = #_of_Machines * Rate * Time, we can say that the amount of work done by 6 machines over 12 days is 6 * r * 12 days = 72r.
If we have only 8 days to do the job, the equation becomes x * r * 8 = 72r where x is the number of machines. x=9 machines, so we need an extra 3 machines (on top of the original 6) to do the job in 8 days.
Approach 2:
If you notice that # of machines and time are inversely proportional (meaning that doubling the machines will cut the time in half), we can quickly solve.
the time goes from 12 days to 8 days, so time was multiplied by 2/3. As a result, # of machines will be multiplied by the inverse, 3/2. So the new # of machines will be 6 * 3/2 = 9 machines. We need an extra 3 machines.
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Approach 1: Plug in a rate for EACH MACHINEjosh80 wrote:Six machines, each working at the same constant rate, together can complete a certain 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?
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Let the rate for each machine = 1 unit per day.
Rate for 6 machines = 6 units per day.
In 12 days, the amount of work produced by 6 machines = r*t = 6*12 = 72 units.
To produce 72 units in 8 days, the required amount of work per day = w/t = 72/8 = 9 units per day.
To increase the rate from 6 units per day to 9 units per day, 3 more machines are needed.
The correct answer is B.
Approach 2: Inverse proportion method
The number of machines is INVERSELY PROPORTIONAL to the number of days:
(machines)(days) = (machines)(days).
As the number of machines INCREASES, the number of days must DECREASE, so that in each case the SAME AMOUNT OF WORK is produced.
Since 6 machines take 12 days, and the job is to be completed in 8 days, we get:
6 * 12 = m * 8
72 = 8m
m = 9.
Since 9 machines are required, the original number of machines -- 6 -- must increase by 3.
The correct answer is B.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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