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Doubt on Rate Problem

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by bobdylan » Fri Apr 27, 2012 3:35 am
I really need some advice on these kind of questions:
1 Question: Six machines, each working at the same constant rate, can complete a job in 12 Days. How many additional machines, each working at the same constant rate, would be required to complete the task in 8 Days?
Solution posted on this site: one machine can do the work in 72 days, so you divide 72 by 8 to get 9. Then you subtract 9 by 6 in order to get 3 machines.

2 Question: 12 identical machines , running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each working at the same constant rate, would be needed to reduce the time required to complete a shipment by 2 days?
Solution on the Manhattan guide: The work of 12 machines is 12 r , so you multiply 12 r by 8 to get 96 r. To figure out how many machines are needed to complete this work in 8-2= 6 days, set up another row and solve for the unkown rate, getting 16 r. Thus, you need 16 machines in total, or 16-12= 4 additional machines.
My doubt is that the 2 look identical, but why you cannot apply the same methodology on both( if you do, the solutions are different)?????
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by niketdoshi123 » Fri Apr 27, 2012 4:36 am
1 Question: Six machines, each working at the same constant rate, can complete a job in 12 Days. How many additional machines, each working at the same constant rate, would be required to complete the task in 8 Days?
Solution:
As number of machines are inversely proportional to days, so if machines are reduced then number of days to complete a job will increase and vice-versa.
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So additional machines required = 9-6=3
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by niketdoshi123 » Fri Apr 27, 2012 4:45 am
2 Question: 12 identical machines , running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each working at the same constant rate, would be needed to reduce the time required to complete a shipment by 2 days?
Image
Additional machines required = 16-12 =4

Did the question the same way and solution is also same..
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by niketdoshi123 » Fri Apr 27, 2012 4:51 am
The work of 12 machines is 12 r
While doing a work-done problem always consider the work = 1 and not any variable such as 'r', this makes your job easier..
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by jrakhe » Fri Apr 27, 2012 3:46 pm
Rate and work problem can be solved using chart. As by using chart it is easy to know what is given and what is missing.
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by neelgandham » Sat Apr 28, 2012 12:13 pm
I am sure that you are not the only one to find work rate questions on the tougher side. To solve these questions easily, remember this work-rate mantra The value of Man(or Machine)-hours(or days) is always equal. What does this mean? It means - The product of the number of men/machines working and the number of work hours is always constant, given that the magnitude of work is constant. Let me solve question 1 using this.

Case 1:
Number of machines = M1 = 6
Number of days required to complete the job = D1 = 12

Case 2:
Number of machines = M2
Number of days the job should be completed in = D2 = 8

According to the above statement, M1*D1 = M2*D2. i.e 6*12 = 8*M2. The value of M2 = 9. So, we need M2-M1 = 9-6 machines to complete the task in 8 days.

Note: If the magnitude of work changes, then we cannot use the formula mentioned above. For example, If the question is 'Six machines, each working at the same constant rate, can complete a job in 12 Days.How many additional machines, each working at the same constant rate, would be required to complete 2 similar tasks in 8 Days?', we should tweak the formula.

(M1*D1)/W1 = (M2*D2)/W2, where W is the magnitude of Work.
6*12/1 = M2*8/2
M2 = 18. So. M2-M1 = 18-6 = 12 additional machines are needed to complete 2 similar tasks in 8 days.

Hope it helps. Let me know if you need any further help.
Last edited by neelgandham on Sat Apr 28, 2012 1:30 pm, edited 1 time in total.
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by GMATGuruNY » Sat Apr 28, 2012 1:20 pm
bobdylan wrote:I really need some advice on these kind of questions:
1 Question: Six machines, each working at the same constant rate, can complete a job in 12 Days. How many additional machines, each working at the same constant rate, would be required to complete the task in 8 Days?
Solution posted on this site: one machine can do the work in 72 days, so you divide 72 by 8 to get 9. Then you subtract 9 by 6 in order to get 3 machines.

2 Question: 12 identical machines , running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each working at the same constant rate, would be needed to reduce the time required to complete a shipment by 2 days?
Solution on the Manhattan guide: The work of 12 machines is 12 r , so you multiply 12 r by 8 to get 96 r. To figure out how many machines are needed to complete this work in 8-2= 6 days, set up another row and solve for the unkown rate, getting 16 r. Thus, you need 16 machines in total, or 16-12= 4 additional machines.
My doubt is that the 2 look identical, but why you cannot apply the same methodology on both( if you do, the solutions are different)?????
Another approach is to plug in a rate for each machine.
I posted a solution to the first problem here:

https://www.beatthegmat.com/six-machines ... 52992.html

I posted a solution to a similar but more complex problem here:

https://www.beatthegmat.com/tv-assemble-t87042.html
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by Danny@GMATAcademy » Sun Jan 08, 2017 10:04 pm
We can use the 'identical machines doing the same job' 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: https://www.youtube.com/watch?v=XOtwd6brDj8
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