Working together, printer A and printer B would finish the

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 \(x\) --> \(x=600\).

Answer: A.

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
questions-from-gmat-prep-practice-exam-please-help-93632.html?hilit=reciprocal%20rate
a-good-one-98479.html?hilit=rate

Hope it helps.
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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

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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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

Answer is A.

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?

\(\frac{1}{A}=\frac{1}{60}\)
\(\frac{1}{B}+\frac{1}{A}=\frac{1}{24}\)

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.

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

Answer: 60(p)=600pages

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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Ta = 60min
Ra = 1/Ta = 1/60
Rb = 1/Tb

Combined task completion time 24min.
=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.

How do you come up with these??

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 \(x\) --> \(x=600\).

Answer: A.
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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

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

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

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)

Another approach after getting rate for B
as rate of B = 1/40
let A prints x pages a minute , then B will print x+5pages a minute
A work for 60 minutes and B work for 40 minutes alone and so ,they are able to print same no. of pages
thus,
40(x+5) = 60x
40x+200 =60x
20x=200
x=10
thus total no of pages = 60x or 40(x+5) =600 pages
Ans A

Given that, A can finish in 60 minutes, combined 24 minutes.
so, the rate of B = 1/24- 1/60 equals 1/40 thus B takes 40 minutes to accomplish the job alone.
As B can finish 5 more pages than A in a minute. Let, A can print x pages per minutes then, B = x+5
60x = 40( x+5)
x= 10
Thus total number of pages together can print = 60 *10

A. 600

Let the total work be 120 units

So, Efficiency of A and B is 5 units/min & Efficiency of A is 2 units/min

Thus , the efficiency of B is 3 units/min

So, 1unit/min = 5 Pages

Hence, 120 Units = 120*5 => 600 Units, Answer must be (A)
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[quote="gauravnagpal"]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


Total task = 60A
B = A+5
24(A+B) = 60A
24(A+A+5) = 60A
24(2A+5)=60A
48A+120= 60A
120=12A
A=10

Total tasks =60A = 600. Check the answers to confirm

Hence option A is the answer.