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It takes printer A 4 more minutes than printer B to print 40

This topic has 3 expert replies and 6 member replies
nhai2003 Senior | Next Rank: 100 Posts Default Avatar
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It takes printer A 4 more minutes than printer B to print 40

Post Sat Jul 11, 2009 2:06 am
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?

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Post Thu Dec 07, 2017 8:05 am
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
Since A and B together can print 50 pages in 6 minutes, their combined rate = w/t = 50/6 = 25/3 pages per minute.

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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Mo2men Legendary Member Default Avatar
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Post Fri Dec 08, 2017 7:50 am
GMATGuruNY wrote:
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
Since A and B together can print 50 pages in 6 minutes, their combined rate = w/t = 50/6 = 25/3 pages per minute.

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.
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

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Post Fri Dec 08, 2017 8:29 am
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
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.
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).

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

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GMAT/MBA Expert

Post Thu Dec 07, 2017 7:21 am
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 have a combined worker problem for which we can use the following formula:

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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Jeffrey Miller Head of GMAT Instruction

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dtweah Master | Next Rank: 500 Posts Default Avatar
Joined
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Posted:
487 messages
Upvotes:
36
Target GMAT Score:
750
Post Sat Jul 11, 2009 8:05 am
nhai2003 wrote:
dtweah wrote:
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

should we start putting x with printer A or B?
Find Rates (page/min) of A and B using 40 pages

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 on
5A^2-28A-96=0

Use quardratic formula

(28+-52)/10=8

Thanks
The Quardratic is

(-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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Thanked by: nhai2003
shibal Master | Next Rank: 500 Posts Default Avatar
Joined
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Posted:
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Test Date:
July XX
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GMAT Score:
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Post Sat Jul 11, 2009 7:28 am
nhai2003 wrote:
dtweah wrote:
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

should we start putting x with printer A or B?
Find Rates (page/min) of A and B using 40 pages

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 on
5A^2-28A-96=0

Use quardratic formula

(28+-52)/10=8

Thanks
28+or- (-28^2-4*5*-96)^1/2 divided by 5*2........

it took me a while to do this exercise... i'm sure there is a shortcut somewhere....

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nhai2003 Senior | Next Rank: 100 Posts Default Avatar
Joined
10 Feb 2009
Posted:
75 messages
Post Sat Jul 11, 2009 5:02 am
dtweah wrote:
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

should we start putting x with printer A or B?
Find Rates (page/min) of A and B using 40 pages

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 on
5A^2-28A-96=0

Use quardratic formula

(28+-52)/10=8

Thanks

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dtweah Master | Next Rank: 500 Posts Default Avatar
Joined
27 Mar 2009
Posted:
487 messages
Upvotes:
36
Target GMAT Score:
750
Post Sat Jul 11, 2009 4:30 am
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

should we start putting x with printer A or B?
Find Rates (page/min) of A and B using 40 pages

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.

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ketkoag Legendary Member Default Avatar
Joined
10 Apr 2008
Posted:
876 messages
Upvotes:
13
Post Sat Jul 11, 2009 4:22 am
lets B takes x mins and therefore A takes x+4 mins.. and then solve it.
Answer would be 24 mins. i.e. d

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