Six machines each working at same constant rate together can

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by knight247 » Thu Sep 15, 2011 10:50 pm
Hey Thouraya,
There are multiple approaches to this problem. I'm sure you know the formula Rate=Work/Time.
If you want to factor in the people involved there is a similar formula you can use. Rate=Work/(People*Time). This kinda makes it a lot easier.

Now in our problem let the work to be done be the printing of 96 pages. Now, here people=machines... Now, whether we have 6 machines or more, the rate that each one works at is the same.

For the 6 machines, we have Rate=96/(6*12) and for the larger number of machines we have 96/(x*8) where x is the number of machines and 8 is the given time as per the problem. Now, both these rates are equal. So 96/(6*12)=96/(x*8)

Solving we get x=9. So 9 machines will finish the job in 8 hrs. 9-6=3 Hence B. All clear?? If you need to know other methods then let me know.

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by Fractal » Thu Sep 22, 2011 10:19 am
Easy approach:

6 Machines --> 12 days
x Machines --> 8 days

8 * 1.5 = 12

so 6 * 1.5 = 9

done in some seconds :-)

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by rooster » Thu Sep 22, 2011 6:23 pm
I set this problem up like this, let me know what you all think.

Since we know this device creates an amount, but the amount is undefined, we set the amount to x. Since we know the number of machines is 6, and the number of days is 12 we can set the equation up like this:

(X/6)= 12 days

Solve for X = 6*12 = 72

Replace X and now set "x" to the number of additional machines, and replace the initial 12 days to 8

72/(6+x) = 8

72= 48 + 8x
24= 8x
3= x

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by Jayanth2689 » Sun Aug 19, 2012 5:56 am
Hey all! I recently learnt another method to tackle this problem! Happy to share:

Original time is t
New time is 2/3t (8/12)

Work = 1

if time is reduced to 2/3, then the rate would have increased to 3/2 -> RT = D -> 3/2 * 2/3 = 1

Thus new machines = 3/2 (Original machines) = 9

additional machines = 3

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by Liarish » Sat Sep 01, 2012 2:44 pm
knight247 wrote:Hey Thouraya,
There are multiple approaches to this problem. I'm sure you know the formula Rate=Work/Time.
If you want to factor in the people involved there is a similar formula you can use. Rate=Work/(People*Time). This kinda makes it a lot easier.

Now in our problem let the work to be done be the printing of 96 pages. Now, here people=machines... Now, whether we have 6 machines or more, the rate that each one works at is the same.

For the 6 machines, we have Rate=96/(6*12) and for the larger number of machines we have 96/(x*8) where x is the number of machines and 8 is the given time as per the problem. Now, both these rates are equal. So 96/(6*12)=96/(x*8)

Solving we get x=9. So 9 machines will finish the job in 8 hrs. 9-6=3 Hence B. All clear?? If you need to know other methods then let me know.

Hey knight247,

Thanks a lot for this formula "Rate=Work/(People*Time)", it has worked perfectly for a number of work questions that I have done. But I was wondering if we could use the same formula for the problem below. Could you please show me how ?

Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ?
1:600
2:800
3:1000
4:1200
5:1500

Answer is : A

Thanks a ton!

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by GMATGuruNY » Sun Sep 02, 2012 12:55 am
Liarish wrote: Hey knight247,

Thanks a lot for this formula "Rate=Work/(People*Time)", it has worked perfectly for a number of work questions that I have done. But I was wondering if we could use the same formula for the problem below. Could you please show me how ?

Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ?
1:600
2:800
3:1000
4:1200
5:1500

Answer is : A

Thanks a ton!
The formula that Knight247 suggested works great for problems in which the number of workers changes.
Here, the number of printers is not changing, so I wouldn't use the formula.
A very efficient approach would be to plug in the answers, which represent the number of pages.
The correct answer choice is almost certainly a multiple of 24 and 60.
Eliminate B, C and E.

Answer choice D: 1200 pages
Rate for A and B together = 1200/24 = 50 pages per minute.
Rate for A alone = 1200/60 = 20 pages per minute.
Rate for B alone = combined rate for A and B - A's rate alone = 50-20 = 30 pages per minute.
B's rate - A's rate = 30-20 = 10 pages per minutes.
Since the difference between B's rate and A's rate must be 5 pages per minute -- HALF the difference here -- the actual number of pages must be 1/2 of 1200.

The correct answer is A.

Note that we had to try only ONE answer choice -- a very efficient way to solve the problem.
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by Turksonaaron » Fri Jun 23, 2017 12:47 pm
GMATGuruNY wrote:
Thouraya wrote:Hi Mitch,

I like your second approach if it always works. I have a question on your first approach, please:

If I want to assume that every machine produces two units (instead of 1), then 6 machines produce 12 units a day, and 12 x 12= 144 units in 12 days.

If I want to produce the 144 units in 8 days instead, then 144/8 ?

Also, I cant cross multiple in work problems cuz I have three variables: days, machines, and units?

Thank you!
The second approach that I used is just a variation of the rate formula: rate * time = work.

In the problem above, rate = number of machines, so (number of machines) * (number of days) = work.

Since the work must remain the same no matter how many machines are used, we get the following inverse proportion:

(number of machines) * (number of days) = (number of machines) * (number of days)

If the number of machines goes up, the number of days must go down, so that the amount of work stays the same. If the number of machines goes down, the number of days must go up, so that the amount of work stays the same. This is the definition of an inverse proportion. As one value goes up, the other goes down, so that the product never changes.

1*30 = 30
2*15 = 30
3*10 = 30
etc.

Regarding the first approach (plugging in for the work being done by each machine), your numbers are correct. If each machine produces 2 units/day, then to complete the job in 9 days, 144/8 = 18 units must be produced each day. Since each machine produces 2 units/day, 9 total machines will be needed, so we'll need to add 3 machines -- the same answer that I got when I plugged in that each machine produces 1 unit/day.

Hope this helps!

(What exactly did you want to cross multiply?)
Hi Mitch

I don't know why Inverse proportion really whips me to the core since high school. How do I attack this monster once and for all

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by GMATGuruNY » Sat Jun 24, 2017 2:34 pm
Turksonaaron wrote:Hi Mitch

I don't know why Inverse proportion really whips me to the core since high school. How do I attack this monster once and for all
Good news: inverse proportions are rarely tested on the GMAT.
That said, here are more practice problems:

Work problems:
https://www.beatthegmat.com/work-problem-t277550.html
https://www.beatthegmat.com/discussing-w ... tml#324983
https://qa.www.beatthegmat.com/rate-problem-t113456.html (second problem)
https://www.beatthegmat.com/four-workers ... 93664.html (second problem)

Non-work problems:
https://www.beatthegmat.com/rate-of-chem ... 88071.html
https://www.beatthegmat.com/proportional ... 95446.html
https://www.beatthegmat.com/algebra-the- ... 90048.html
https://www.beatthegmat.com/formula-t117058.html
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by Scott@TargetTestPrep » Fri Jun 30, 2017 8:18 am
imane81 wrote:
Six machines each working at 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
We are given that six machines, each working at the same constant rate, together can complete a certain job in 12 days. Since rate = work/time, and if we consider work as 1, the rate of the six machines is 1/12.

We need to determine how many additional machines each working at the same constant rate will be needed to complete the same job in 8 days. In other words, we need to determine how many additional machines are needed to work at a rate of 1/8. Since each machine works at the same constant rate, we can use a proportion to first determine the number of machines needed to work at the rate of 1/8.

Our proportion is as follows: 6 machines is to a rate of 1/12 as x machines is to a rate of 1/8.

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

72 = 8x

x = 9

So, we need 9 - 6 = 3 more machines.

Answer: B

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