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# Working together, printer A and printer B would finish the

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Working together, printer A and printer B would finish the [#permalink]

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01 Sep 2010, 10:12
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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 ?

A. 600
B. 800
C. 1000
D. 1200
E. 1500

[Reveal] Spoiler:
I know this question is relatively symol if make an equation in one vaibale ...
I tried to do it by applying the fundamental of A = Jobs per min * time ( the way we typically solve the work problems ) and i was stuck

I did jobs per minute A , 1/60
combined rate = 1/24

so rate of b = 1/24 - 1/60 = 1/40

but could not arrive at the solution ... i tried to form the equation by assuming x as the total numbe of pages So x/60+ x+5/40 = cld nt take ot forward from here
kindly see where am I losing the track !
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Sep 2012, 09:01, edited 2 times in total.
Edited the question.
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01 Sep 2010, 11:56
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gauravnagpal wrote:
.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 ?

a. 600
b. 800
c. 1000
d. 1200
e. 1500

I know this question is relatively symol if make an equation in one vaibale ...
I tried to do it by applying the fundamental of A = Jobs per min * time ( the way we typically solve the work problems ) and i was stuck

I did jobs per minute A , 1/60
combined rate = 1/24

so rate of b = 1/24 - 1/60 = 1/40

but could not arrive at the solution ... i tried to form the equation by assuming x as the total numbe of pages So x/60+ x+5/40 = cld nt take ot forward from here
kindly see where am I losing the track !

Let the rate of printer A be $$a$$ pages per minute, the rate of printer B be $$b$$ pages per minute and whole task be $$x$$ pages.

$$time*rate=job \ done$$:

Working together, printer A and printer B would finish the task in 24 minutes" --> $$24(a+b)=x$$;
Printer A alone would finish the task in 60 minutes --> $$60a=x$$;
Printer B prints 5 pages a minute more than printer A --> $$b=a+5$$.

Solving for $$x$$ --> $$x=600$$.

Some work problems with solutions:
time-n-work-problem-82718.html?hilit=reciprocal%20rate
facing-problem-with-this-question-91187.html?highlight=rate+reciprocal
what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal
gmat-prep-ps-93365.html?hilit=reciprocal%20rate
a-good-one-98479.html?hilit=rate

Hope it helps.
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03 Sep 2010, 10:26
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B in a minute=x/40
A in a minute=x/60
then,
x/40-x/60=5

Solving x=600
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06 Sep 2012, 07:09
1
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Bunuel wrote:
gauravnagpal wrote:
.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 ?

a. 600
b. 800
c. 1000
d. 1200
e. 1500

I know this question is relatively symol if make an equation in one vaibale ...
I tried to do it by applying the fundamental of A = Jobs per min * time ( the way we typically solve the work problems ) and i was stuck

I did jobs per minute A , 1/60
combined rate = 1/24

so rate of b = 1/24 - 1/60 = 1/40

but could not arrive at the solution ... i tried to form the equation by assuming x as the total numbe of pages So x/60+ x+5/40 = cld nt take ot forward from here
kindly see where am I losing the track !

Let the rate of printer A be $$a$$ pages per minute, the rate of printer B be $$b$$ pages per minute and whole task be $$x$$ pages.

$$time*rate=job \ done$$:

Working together, printer A and printer B would finish the task in 24 minutes" --> $$24(a+b)=x$$;
Printer A alone would finish the task in 60 minutes --> $$60a=x$$;
Printer B prints 5 pages a minute more than printer A --> $$b=a+5$$.

Solving for $$x$$ --> $$x=600$$.

Some work problems with solutions:
time-n-work-problem-82718.html?hilit=reciprocal%20rate
facing-problem-with-this-question-91187.html?highlight=rate+reciprocal
what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal
gmat-prep-ps-93365.html?hilit=reciprocal%20rate
a-good-one-98479.html?hilit=rate

Hope it helps.

Hi Bunnel,

I have always one confusion in rate and work problems can you please clarify this?,

When do we add rates i.e what you did above...... $$24(a+b)=x$$;

and when do we divide by rates i.e something . rate =(Job done/ time)

Regards

Srinath
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06 Sep 2012, 09:39
Expert's post
1
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kotela wrote:
Bunuel wrote:
gauravnagpal wrote:
.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 ?

a. 600
b. 800
c. 1000
d. 1200
e. 1500

I know this question is relatively symol if make an equation in one vaibale ...
I tried to do it by applying the fundamental of A = Jobs per min * time ( the way we typically solve the work problems ) and i was stuck

I did jobs per minute A , 1/60
combined rate = 1/24

so rate of b = 1/24 - 1/60 = 1/40

but could not arrive at the solution ... i tried to form the equation by assuming x as the total numbe of pages So x/60+ x+5/40 = cld nt take ot forward from here
kindly see where am I losing the track !

Let the rate of printer A be $$a$$ pages per minute, the rate of printer B be $$b$$ pages per minute and whole task be $$x$$ pages.

$$time*rate=job \ done$$:

Working together, printer A and printer B would finish the task in 24 minutes" --> $$24(a+b)=x$$;
Printer A alone would finish the task in 60 minutes --> $$60a=x$$;
Printer B prints 5 pages a minute more than printer A --> $$b=a+5$$.

Solving for $$x$$ --> $$x=600$$.

Some work problems with solutions:
time-n-work-problem-82718.html?hilit=reciprocal%20rate
facing-problem-with-this-question-91187.html?highlight=rate+reciprocal
what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal
gmat-prep-ps-93365.html?hilit=reciprocal%20rate
a-good-one-98479.html?hilit=rate

Hope it helps.

Hi Bunnel,

I have always one confusion in rate and work problems can you please clarify this?,

When do we add rates i.e what you did above...... $$24(a+b)=x$$;

and when do we divide by rates i.e something . rate =(Job done/ time)

Regards

Srinath

You can denote rate directly by some variable (a in the solution) or express rate as a reciprocal of time. For example, say printer A needs t minutes to print 1 page and printer B needs m minutes to print 1 page, then the rate of printer A would be job/time=1/t pages per minute and the rate of printer B would be 1/m pages per minute (rate is a reciprocal of time, so 1/t=a and 1/m=b). In this case the equation would be 24(1/t+1/m)=x.

Hope it's clear.
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Re: Working together, printer A and printer B would finish the [#permalink]

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08 Sep 2012, 04:51
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First thing i did was i found out time that is required to B to complete the task alone: 1/24-1/60=3/120=1/40. Then i looked at the information which states that the rate of B is 5+ page than that of A so, lets say x is the number of pages printed by A per minute, so the task consists of 60*x or 40*(x+5) pages. I can make an equation: 60x=40(x+5), 20x=200, x=10, total number of pages is 60*10=600 or 40*15=600

It is clear but it took me about 3 min to do it, does it because i am doing it slow or i am using longer route?
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15 Nov 2012, 04:37
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$$\frac{1}{A}=\frac{1}{60}$$
$$\frac{1}{B}+\frac{1}{A}=\frac{1}{24}$$

Get: $$\frac{1}{B}$$

$$\frac{1}{B}=\frac{1}{24}-\frac{1}{60}=\frac{1}{40}$$

Let p be the number of pages produced by A.
Let p+5 be the number of pages produced by B.

$$24(p + p+5) = 60(p)==> p=10pages$$

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Re: Working together, printer A and printer B would finish the [#permalink]

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03 Mar 2013, 23:40
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gauravnagpal wrote:
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 ?

A. 600
B. 800
C. 1000
D. 1200
E. 1500

[Reveal] Spoiler:
I know this question is relatively symol if make an equation in one vaibale ...
I tried to do it by applying the fundamental of A = Jobs per min * time ( the way we typically solve the work problems ) and i was stuck

I did jobs per minute A , 1/60
combined rate = 1/24

so rate of b = 1/24 - 1/60 = 1/40

but could not arrive at the solution ... i tried to form the equation by assuming x as the total numbe of pages So x/60+ x+5/40 = cld nt take ot forward from here
kindly see where am I losing the track !

total time taken by B = 24 * 60 / (60 -24) = 40 min.

A take 60 min. B takes 40 min to complete a task.

Now, divide the values given in option (in Ans) to get the rate per min.

option A: 600 / 10 = 60 & 600/40 = 15...> this satisfies the condition given in question stem that printer B prints 5 pages a minute more than printer A ?
. therefore A
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Re: Working together, printer A and printer B would finish the [#permalink]

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21 Sep 2013, 10:31
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Ta = 60min
Ra = 1/Ta = 1/60
Rb = 1/Tb

=Ra + Rb
=1/60 + 1/Tb = 1/24
Tb = 40 min.

Ra = X/Ta Rb = X/Tb

Ra + 5 = Rb
X/Ta + 5 = X/Tb
X/60 + 5 = X/40
X=600 Ans.
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Re: Working together, printer A and printer B would finish the [#permalink]

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25 Sep 2013, 03:09
mbaiseasy wrote:
Let p be the number of pages produced by A.
Let p+5 be the number of pages produced by B.

$$24(p + p+5) = 60(p)==> p=10pages$$

How do you come up with these??
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20 Nov 2013, 15:01
Bunuel wrote:
gauravnagpal wrote:
.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 ?

a. 600
b. 800
c. 1000
d. 1200
e. 1500

I know this question is relatively symol if make an equation in one vaibale ...
I tried to do it by applying the fundamental of A = Jobs per min * time ( the way we typically solve the work problems ) and i was stuck

I did jobs per minute A , 1/60
combined rate = 1/24

so rate of b = 1/24 - 1/60 = 1/40

but could not arrive at the solution ... i tried to form the equation by assuming x as the total numbe of pages So x/60+ x+5/40 = cld nt take ot forward from here
kindly see where am I losing the track !

Let the rate of printer A be $$a$$ pages per minute, the rate of printer B be $$b$$ pages per minute and whole task be $$x$$ pages.

$$time*rate=job \ done$$:

Working together, printer A and printer B would finish the task in 24 minutes" --> $$24(a+b)=x$$;
Printer A alone would finish the task in 60 minutes --> $$60a=x$$;
Printer B prints 5 pages a minute more than printer A --> $$b=a+5$$.

Solving for $$x$$ --> $$x=600$$.

Some work problems with solutions:
time-n-work-problem-82718.html?hilit=reciprocal%20rate
facing-problem-with-this-question-91187.html?highlight=rate+reciprocal
what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal
gmat-prep-ps-93365.html?hilit=reciprocal%20rate
a-good-one-98479.html?hilit=rate

Hope it helps.

I'm curious about the 1/a+1/b=1/24 solution as well. I started out trying that way and got stuck at the same point as the other fellow. Is there any way to solve it once you have 1/60+1/40 for their combined rates? Or is that just a dead end?

edit: Also, question #2:

Shouldn't the equation be 24(1/a+1/b)=x; ? Since you have 24 minutes in which the machines are working at their individual rates, doing 1/a and 1/b of the job per minute? I don't get how one can know when to arbitrarily use "a" instead of '1/a" or "b" instead of "1/b"
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21 Nov 2013, 01:40
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AccipiterQ wrote:
Bunuel wrote:
gauravnagpal wrote:
.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 ?

a. 600
b. 800
c. 1000
d. 1200
e. 1500

I know this question is relatively symol if make an equation in one vaibale ...
I tried to do it by applying the fundamental of A = Jobs per min * time ( the way we typically solve the work problems ) and i was stuck

I did jobs per minute A , 1/60
combined rate = 1/24

so rate of b = 1/24 - 1/60 = 1/40

but could not arrive at the solution ... i tried to form the equation by assuming x as the total numbe of pages So x/60+ x+5/40 = cld nt take ot forward from here
kindly see where am I losing the track !

Let the rate of printer A be $$a$$ pages per minute, the rate of printer B be $$b$$ pages per minute and whole task be $$x$$ pages.

$$time*rate=job \ done$$:

Working together, printer A and printer B would finish the task in 24 minutes" --> $$24(a+b)=x$$;
Printer A alone would finish the task in 60 minutes --> $$60a=x$$;
Printer B prints 5 pages a minute more than printer A --> $$b=a+5$$.

Solving for $$x$$ --> $$x=600$$.

Some work problems with solutions:
time-n-work-problem-82718.html?hilit=reciprocal%20rate
facing-problem-with-this-question-91187.html?highlight=rate+reciprocal
what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal
gmat-prep-ps-93365.html?hilit=reciprocal%20rate
a-good-one-98479.html?hilit=rate

Hope it helps.

I'm curious about the 1/a+1/b=1/24 solution as well. I started out trying that way and got stuck at the same point as the other fellow. Is there any way to solve it once you have 1/60+1/40 for their combined rates? Or is that just a dead end?

edit: Also, question #2:

Shouldn't the equation be 24(1/a+1/b)=x; ? Since you have 24 minutes in which the machines are working at their individual rates, doing 1/a and 1/b of the job per minute? I don't get how one can know when to arbitrarily use "a" instead of '1/a" or "b" instead of "1/b"

In this case we'd have:
The rate of printer A = 1/a pages per minute, where a is the time to print 1 page.
The rate of printer B = 1/b pages per minute, where b is the time to print 1 page.

Working together, printer A and printer B would finish the task in 24 minutes" --> $$24(\frac{1}{a}+\frac{1}{b})=x$$;
Printer A alone would finish the task in 60 minutes --> $$60*\frac{1}{a}=x$$;
Printer B prints 5 pages a minute more than printer A --> $$\frac{1}{b}=\frac{1}{a}+5$$.

Solving for $$x$$ --> $$x=600$$.

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Re: Working together, printer A and printer B would finish the [#permalink]

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18 Mar 2014, 06:00
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Rate A= X
Rate B= X+5

Work(A)=> X * 60 = 60X

Rate(A+B) * 24 = Work

(2X+5) * 24 = 60X

X=10
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Re: Working together, printer A and printer B would finish the [#permalink]

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22 Apr 2014, 20:56
A does in one minute =x pages
Therefore, in 60 minutes=60x pages

B does in one minute= x+5
In 24 minutes both do 60x pages
24x+24(x+5)=60x
X=10 total work=60*10=600 pages
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Re: Working together, printer A and printer B would finish the [#permalink]

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15 May 2014, 10:02
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Easiest way to do this: Machine A and B can do the task in 24 minutes thus Rate of A and B = 1/24. Now given A can do the task in 60 minutes therefore Rate of A= 1/60. We know that Rate of A and B = Rate of A + Rate of B therefore Rate of B= Rate of A and B - Rate of A = 1/24-1/60= 1/40. Now we know that Rate of B = 1/40 thus B can do the work in 40 minutes.

Let pages printed per minute by A = x, given that pages printed by B per minute is 5 more than that of A
Pages printed by B per minute = x+5
Now Complete task is done by A in 60 minutes therefore total number of pages printed by A = x * 60
Also Complete task is done by B in 40 minutes therefore total number of pages printed by B = (x+5) * 40
therefore x * 60 = (x+5) * 40
therefore x=10
thus the total number of pages in task = x*60 = 10*60 = 600
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Re: Working together, printer A and printer B would finish the [#permalink]

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13 Jun 2016, 00:49
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Re: Working together, printer A and printer B would finish the [#permalink]

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18 Jul 2016, 04:29
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gauravnagpal wrote:
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 ?

A. 600
B. 800
C. 1000
D. 1200
E. 1500

[Reveal] Spoiler:
I know this question is relatively symol if make an equation in one vaibale ...
I tried to do it by applying the fundamental of A = Jobs per min * time ( the way we typically solve the work problems ) and i was stuck

I did jobs per minute A , 1/60
combined rate = 1/24

so rate of b = 1/24 - 1/60 = 1/40

but could not arrive at the solution ... i tried to form the equation by assuming x as the total numbe of pages So x/60+ x+5/40 = cld nt take ot forward from here
kindly see where am I losing the track !

Okay..this is how I did it..
Let the task(number of pages) be 120x(LCM of all numbers given in the problem)..

A and B take 24 minutes to complete it..thus, pages per min = 5x
A's pages per minute = 2x
B's pages per minute = 3x

Difference
3x - 2x = 5
=> x = 5
Thus, 120x = 600..(A)

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Re: Working together, printer A and printer B would finish the   [#permalink] 18 Jul 2016, 04:29
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