Work Problem: It takes printer A 4 more mins than Printer B

[ramanalokanathan]

I saw this problem in gmatclub forum. Few questions:

1. Is there an easier / straight forward way to solve this problem
2. What is the general strategy to setup the equations for "working together" problems like this.

Appreciate your response.

---

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?

A. 12
B. 18
C. 20
D. 24
E. 30

[jatharnikhil]

Hello,

Lets consider B takes 'X' minutes to print 40 pages.
Then A takes 'X+4' minutes to print 40 pages.

then, per pages per minute by A => 40/(X+4), B => 40/(X).
Add both, then pages per minute by both A, B => 40/(X+4) + 40/(X).

Now, in 6 min both print 50 pages. [ 40/(X+4) + 40/(X) ] * 6 = 50.

calculate value of X.

Let me know if you know any better method.

-
Kind Regards,
Nikhil J.
student/GMAT Enthu/ http://www.nikhilj.com

[Ben Ku]

The rate in a work problem is expressed as "job done / time". In this case, if it takes printer B x minutes to print 40 pages, then the rates for the printers are:
A: 40 / (x + 4)
B: 40 / x
A+B: 50 /6
When we have two things working together, we can add their rates:
[40 / (x + 4)] + (40 / x) = (50 / 6)

Solving this, you get x = 8 (we can rule out -2.5)
So it takes printer A 12 minutes to print 40 pages, it will take it 24 minutes to print 80 pages. The answer is (D).

[aliag916]

Hello,
I understand the above solution, but how to arrive at x=8?
When I solve the equation I get : 5x^2 -28x - 96 = 0
Can anyone pls explain how to get x = 8 from the above.

Thank u!

[RonPurewal]

Hello,
I understand the above solution, but how to arrive at x=8?
When I solve the equation I get : 5x^2 -28x - 96 = 0
Can anyone pls explain how to get x = 8 from the above.

Thank u!

Well, if you factor that equation, it factors to (x - 8) times (5x + 12).
But, GMAC will not ask you to do that kind of factoring.
In fact, I've never seen a factoring problem with a number other than "1" attached to x^2, unless it's some "special" pattern, e.g., 9x^2 - 25y^2 = (3x - 5y)(3x + 5y).

If I saw this problem, I would just guess integer values of x, and feed them into the original equation (the one with the fractions in it, not the quadratic).
I'd start with factors of 40, because you're dividing 40 by things on the left.
Once I got to 8 -- which wouldn't take long, if I were trying factors of 40 -- I'd get 40/12 + 40/8 = 25/3. That's 10/3 + 5 = 25/3, which is a true statement. Done.

[RonPurewal]

In any case -- Further discussion of this problem is not allowed until the ORIGINAL SOURCE is posted.

Forums are not original sources, so "I saw this problem on gmatclub forum" is not an acceptable citation. We need original authorship, please.

If anyone knows the source, please cite it. If not, we'll eventually have to lock or delete the thread.

[aliag916]

Thank u! very clearly explained.
This is from one of Ron's class sessions.

[RonPurewal]

Thank u! very clearly explained.
This is from one of Ron's class sessions.

This exact problem?
Hmm...
I don't remember it, but, then again, I'm really bad at remembering things.

What was the date and/or the title of the session?

Thanks.

[aliag916]

It's Feb 2, 2012 Rates Problem. Yes, it's the exact same problem and you do say that its not an official problem.

[RonPurewal]

It's Feb 2, 2012 Rates Problem. Yes, it's the exact same problem and you do say that its not an official problem.

Hmm. Thanks.