It takes printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take printer A to print 80 pages?
* 12
* 18
* 20
* 24
* 30
should we start putting x with printer A or B?
It takes printer A 4 more minutes than printer B to print 40
This topic has expert replies
Find Rates (page/min) of A and B using 40 pagesnhai2003 wrote:It takes printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take printer A to print 80 pages?
* 12
* 18
* 20
* 24
* 30
should we start putting x with printer A or B?
A B
40/A+4 40/A
When they work together on 50 pages ( Pages/page/min)=Time in min
Since they work together combine their rates
50/(40 (1/A+4 +1/A))=6
5A^2-28A-96=0
Use quardratic formula
(28+-52)/10=8
A=8, this is B's time
8+4 =12mins A's time
If A can do 40 in 12mins then it will do 80 in 24mins
Hence D.
Dtweah can you elaborate more ondtweah wrote:Find Rates (page/min) of A and B using 40 pagesnhai2003 wrote:It takes printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take printer A to print 80 pages?
* 12
* 18
* 20
* 24
* 30
should we start putting x with printer A or B?
A B
40/A+4 40/A
When they work together on 50 pages ( Pages/page/min)=Time in min
Since they work together combine their rates
50/(40 (1/A+4 +1/A))=6
5A^2-28A-96=0
Use quardratic formula
(28+-52)/10=8
A=8, this is B's time
8+4 =12mins A's time
If A can do 40 in 12mins then it will do 80 in 24mins
Hence D.
5A^2-28A-96=0
Use quardratic formula
(28+-52)/10=8
Thanks
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28+or- (-28^2-4*5*-96)^1/2 divided by 5*2........nhai2003 wrote:Dtweah can you elaborate more ondtweah wrote:Find Rates (page/min) of A and B using 40 pagesnhai2003 wrote:It takes printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take printer A to print 80 pages?
* 12
* 18
* 20
* 24
* 30
should we start putting x with printer A or B?
A B
40/A+4 40/A
When they work together on 50 pages ( Pages/page/min)=Time in min
Since they work together combine their rates
50/(40 (1/A+4 +1/A))=6
5A^2-28A-96=0
Use quardratic formula
(28+-52)/10=8
A=8, this is B's time
8+4 =12mins A's time
If A can do 40 in 12mins then it will do 80 in 24mins
Hence D.
5A^2-28A-96=0
Use quardratic formula
(28+-52)/10=8
Thanks
it took me a while to do this exercise... i'm sure there is a shortcut somewhere....
The Quardratic isnhai2003 wrote:Dtweah can you elaborate more ondtweah wrote:Find Rates (page/min) of A and B using 40 pagesnhai2003 wrote:It takes printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take printer A to print 80 pages?
* 12
* 18
* 20
* 24
* 30
should we start putting x with printer A or B?
A B
40/A+4 40/A
When they work together on 50 pages ( Pages/page/min)=Time in min
Since they work together combine their rates
50/(40 (1/A+4 +1/A))=6
5A^2-28A-96=0
Use quardratic formula
(28+-52)/10=8
A=8, this is B's time
8+4 =12mins A's time
If A can do 40 in 12mins then it will do 80 in 24mins
Hence D.
5A^2-28A-96=0
Use quardratic formula
(28+-52)/10=8
Thanks
(-b+-(b^2-4ac)^.5)/2a
b=-28
A=5
c=-96
(28- (28^2-4 x 5 x -96)^.5)/2 x 5
(28-+(784+1920)^.5)/10
28-+(2704)^.5)/10 ( Since u know 50^2=2500, 52^2 =2704)
(28+52)/10 (reject negative answer)
hope this helps
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We have a combined worker problem for which we can use the following formula:nhai2003 wrote:It takes printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take printer A to print 80 pages?
* 12
* 18
* 20
* 24
* 30
work ( machine 1) + work ( machine 2) = total work completed
We are given that it takes printer A 4 more minutes than printer B to print 40 pages. Recall that rate = work/time, and if we let the rate of printer B = 40/t, in which t is the time for printer B to print 40 pages, then the rate of printer A = 40/(t+4).
We are also given that working together the two printers can print 50 pages in 6 minutes.
Since work = rate x time, we can calculate the work done by each printer.
printer A work = 40/(t+4) x 6 = 240/(t+4)
printer B work = 40/t x 6 = 240/t
Since the two machines print 50 pages together, we can use that value in our combined work formula and determine t.
work (printer A) + work (printer B) = 50 pages
240/(t+4) + 240/t = 50
Multiplying the entire equation by t(t+4) gives us:
240t + 240(t+4) = 50t(t+4)
240t + 240t + 960 = 50t^2 + 200t
50t^2 - 280t - 960 = 0
5t^2 - 28t - 96 = 0
(5t + 12)(t - 8) = 0
t = -12/5 or t = 8
Since t can't be negative, t = 8. That is, it takes printer B 8 minutes to print 40 pages. Thus it will take printer A 12 minutes to print 40 pages and 24 minutes to print 80 pages (since 80 pages are twice as many as 40 pages).
Answer: D
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Since A and B together can print 50 pages in 6 minutes, their combined rate = w/t = 50/6 = 25/3 pages per minute.nhai2003 wrote:It takes printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take printer A to print 80 pages?
* 12
* 18
* 20
* 24
* 30
We can PLUG IN THE ANSWERS, which represent A's time to print 80 pages.
When the correct answer choice is plugged in, the combined rate for A and B will be 25/3 pages per minute.
D: 24 minutes
Here, A takes 24 minutes to print 80 pages, implying that A's time to print 40 pages = 12 minutes.
Thus, A's rate = w/t = 40/12 = 10/3 pages per minute.
Since A takes 4 more minutes than B to print 40 pages, B's time to print 40 pages = 12-4 = 8 minutes.
Thus, B's rate = w/t = 40/8 = 5 pages per minute.
Combined rate for A and B = 10/3 + 5 = 10/3 + 15/3 = 25/3 pages per minute.
Success!
The correct answer is: D.
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Dear Mitch,GMATGuruNY wrote:Since A and B together can print 50 pages in 6 minutes, their combined rate = w/t = 50/6 = 25/3 pages per minute.nhai2003 wrote:It takes printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take printer A to print 80 pages?
* 12
* 18
* 20
* 24
* 30
We can PLUG IN THE ANSWERS, which represent A's time to print 80 pages.
When the correct answer choice is plugged in, the combined rate for A and B will be 25/3 pages per minute.
D: 24 minutes
Here, A takes 24 minutes to print 80 pages, implying that A's time to print 40 pages = 12 minutes.
Thus, A's rate = w/t = 40/12 = 10/3 pages per minute.
Since A takes 4 more minutes than B to print 40 pages, B's time to print 40 pages = 12-4 = 8 minutes.
Thus, B's rate = w/t = 40/8 = 5 pages per minute.
Combined rate for A and B = 10/3 + 5 = 10/3 + 15/3 = 25/3 pages per minute.
Success!
The correct answer is: D.
i have conceptual question here
If B takes T minutes to produce 40 pages, then A takes (T+4) minutes to produce same 40 pages.
If B takes 2T minutes to produce 80 pages, then does A take to produce same 80 pages: 2(T+4)minutes or (2T +4 ) minutes??
Thanks
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If the amount of work is multiplied by factor of x -- and the rate stays constant -- then the time must also be multiplied by a factor of x.Mo2men wrote:Dear Mitch,
i have conceptual question here
If B takes T minutes to produce 40 pages, then A takes (T+4) minutes to produce same 40 pages.
If B takes 2T minutes to produce 80 pages, then does A take to produce same 80 pages: 2(T+4)minutes or (2T +4 ) minutes??
Thanks
Thus:
If A takes T+4 minutes to produce 40 pages, then the number of minutes for A to produce 80 pages -- twice the amount of work -- is 2(T+4).
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As a tutor, I don't simply teach you how I would approach problems.
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For more information, please email me (Mitch Hunt) at [email protected].
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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