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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: 220
Location: India
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 349 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.

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Intern
Joined: 19 Jun 2017
Posts: 4
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: 122
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
Re: Twelve identical machines, running continuously at the same &nbs [#permalink] 07 Aug 2017, 11:39

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