When working together, printers A and B can finish printing the entire

When working together, printers A and B can finish printing the entire document in 24 minutes. If printer A by itself can finish printing the document in 60 minutes, how many pages does the document have if printer B prints 5 pages more per minute than printer A?

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


Let \(a\) denote the number of pages Printer A prints in one minute.

Let \(b\) denote the number of pages Printer B prints in one minute.

Given that printers A and B together can print the entire document in 24 minutes, the total number of pages in the document is \(24a + 24b\).

However, when Printer A works alone, it completes the document in 60 minutes, implying the document consists of \(60a\) pages.

Thus, \(24a + 24b = 60a\). Given that \(b = a + 5\), we would get \(24a + 24(a + 5) = 60a\), which results in \(a=10\).

Therefore, the document has \(60a=600\) pages.


Answer: A

Hope it helps.
_________________

B in a minute=x/40
A in a minute=x/60
then,
x/40-x/60=5

Solving x=600

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
_________________

Rate A= X
Rate B= X+5

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

Rate(A+B) * 24 = Work

(2X+5) * 24 = 60X

X=10

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)

Solution:

We can let x = the number of minutes it takes printer B to finish the task by itself and create the equation:

1/60 + 1/x = 1/24

Multiplying both sides of the equation by 120x, we have:

2x+ 120 = 5x

120 = 3x

40 = x

Now, if we let n = the total number of pages the task has and since printer B prints 5 pages a minute more than printer A, we can recreate the equation:

n/60 + 5 = n/40

Multiplying both sides of the equation by 120, we have:

2n + 600 = 3n

600 = n

Answer: A
_________________

Why on earth would we not use PITA (Plugging In The Answers) rather than doing the algebra?!?! You get zero bonus points for doing the "real" math. The GMAT is not a math test. It is a test of whether you can get the right answers quickly, efficiently, without causing yourself fatigue, and without setting yourself up to make careless mistakes.

We know we need to be a multiple of 24 and of 60. B, C, and E are wrong. Cool, down to A and D. A looks easier to work with, so let's try that.

If the task is to print 600 pages and A can finish in 60 minutes, A prints 10 pages per minute. B prints 5 pages per minute more than A, so B prints 15 pages per minute. Together, they print 25 pages per minute. If they work together for 24 minutes, will they finish the 600 pages? Yep.

Answer choice A.


ThatDudeKnowsPITA

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

For A: W = W | R = W/60 | T = 60 mins
For B: W = W | R = (W/60)+5 | T = t

Combined W rate = 24 mins
W = [W/60 + (W/60)+5]*24 (W=RT)

Upon simplifying we get,

60W = [(2W + 300)/60]*24
12W = 7200
W = 600 pages