Problem Solving

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)?????

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.

So additional machines required = 9-6=3

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?

Additional machines required = 16-12 =4

Did the question the same way and solution is also same..

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..

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.

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.

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

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