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# Twelve identical machines, running continuously at the same

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Manager
Joined: 25 Jun 2016
Posts: 61
GMAT 1: 780 Q51 V46
Re: Twelve identical machines, running continuously at the same  [#permalink]

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08 Jan 2017, 22:53
We can use the 'identical machines' formula (old # of machines)(old time) = (new # of machines)(new time)

Plugging in, we get:

(12)(8) = (new #)(6) -->
(2)(8) = new # -->
16 = new #

So we need sixteen machines to do the job in 6 days. In other words we need 4 additional machines.

You can find an in-depth explanation of the formula used above here:

Manager
Joined: 12 Jun 2016
Posts: 212
Location: India
Concentration: Technology, Leadership
WE: Sales (Telecommunications)
Re: Twelve identical machines, running continuously at the same  [#permalink]

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11 Jul 2017, 07:15
Can also be solved by Using RTD chart. From the chart (See attachment) we get

$$(12+x) * \frac{1}{(12*8)} * 6 = 1$$

$$(12+x) = 16$$

x = 4
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MGMAT_Wold Problem_6.png [ 16.92 KiB | Viewed 653 times ]

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Re: Twelve identical machines, running continuously at the same  [#permalink]

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12 Jul 2017, 17:12
gsaxena26 wrote:
Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days?

A. 2
B. 3
C. 4
D. 6
E. 9

We are given that 12 machines have a rate of 1/8. We want the shipment to be completed in 6 days, which means that the rate would be ⅙. We need to determine the number of machines necessary to have that rate of 1/6. We can create the following proportion in which n = the new number of machines:

12/(1/8) = n(/1/6)

Multiplying the left side by 8/8 and the right side by 6/6, we get:

96 = 6n

16 = n

Thus, there would need to be 4 additional machines.

Answer: C
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Joined: 19 Jun 2017
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GMAT 1: 720 Q49 V38
Re: Twelve identical machines, running continuously at the same  [#permalink]

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07 Aug 2017, 10:12
Let total work done by 12 workers for 8 days= 96 units( multiple of 12 and 8) To make division faster and easier
Work done by 12 workers per day = 96/8= 12 units
Work done by each worker per day = 12/12= 1 unit

Now 96 unit of work needs to be completed in 6 days
So per day work = 96/6= 16 units
With the rate of 1 unit/ day it will take 16 workers to achieve a rate of 16 units/ day

So number of workers have to be increased from 12 to 16 hence an increase of 4 workers.
Manager
Joined: 24 Jun 2017
Posts: 120
Re: Twelve identical machines, running continuously at the same  [#permalink]

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07 Aug 2017, 11:39
12 machines in 8 days produce 96 amount of work
so 96 = 12 * 8
keeping same needed amount of work how many more machines should be taken aboard to produce 96 in 6 days

96 = (12 +x) 6
96 =72 + 6x
24 = 6x
x = 4
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Re: Twelve identical machines, running continuously at the same  [#permalink]

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23 Nov 2018, 12:42
Hi All,

We're told that twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. We're asked how many ADDITIONAL machines, each running at the same constant rate, would be needed to REDUCE the time required to complete a shipment BY two days.

In these types of 'work' questions, it often helps to calculate the total amount of work needed, then consider the other variables involved. Here, since we have 12 machines EACH working for 8 days, the total amount of work to complete a shipment would be...

(12 machines)(8 days each) = 96 machine-days of work

Thus, 1 machine would need 96 days to complete the job
2 machines would need 48 days each to complete the job
3 machines would need 32 days each to complete the job
Etc.

We're asked to reduce the total time by 2 days, meaning that the job should take 6 days to complete. That would require...
(96 machine days of work)/(6 total days) = 16 machines needed, each working for 6 days. We already have 12 machines, so we would need 4 more machines.

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Re: Twelve identical machines, running continuously at the same   [#permalink] 23 Nov 2018, 12:42

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