• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

## Running at their respective constant rates, machine X takes

tagged by: Brent@GMATPrepNow

This topic has 4 expert replies and 0 member replies
BTGmoderatorRO Moderator
Joined
30 Aug 2017
Posted:
770 messages
Followed by:
6 members

#### Running at their respective constant rates, machine X takes

Thu Mar 01, 2018 12:43 pm
Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets.

A. 4
B. 6
C. 8
D. 10
E. 12
OA is E
Experts, may you help me here? I am confused. What formulas should I set here?

### GMAT/MBA Expert

mbawisdom Senior | Next Rank: 100 Posts
Joined
16 Dec 2014
Posted:
94 messages
Followed by:
4 members
2
GMAT Score:
770
Mon Mar 05, 2018 7:49 am
Roland2rule wrote:
Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets.

A. 4
B. 6
C. 8
D. 10
E. 12
OA is E
Experts, may you help me here? I am confused. What formulas should I set here?
Work = Rate * Time

Machine X:
w = Rx * T
Rx = w/T

Machine Y:
w = Ry * (T-2)
Ry = w/(T-2)

Situation from question:

5w/4 = (Rx + Ry)*3
5w/4 = [w/T + w/(T-2)]*3 --> we can divide through by W
5/4 = [1/T + 1/(T-2)]*3
5/12 = 1/T + 1/(T-2)
5(T)(T-2) = 12(T-2) + 12(T)
5T^2 - 10T = 24T - 24
5T^2 - 34T + 24 = 0
(T-6)(5T-4) = 0

T must be > 2 so the only solution is T = 6

Machine X can produce w widgets in T so it must be able to produce 2w widgets in 2T; given T= 6 then the answer is 2*6 = 12

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
1209 messages
Followed by:
8 members
43
Tue Mar 06, 2018 9:18 am
Roland2rule wrote:
Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets.

A. 4
B. 6
C. 8
D. 10
E. 12
We can let x = the number of days it takes Machine X to produce w widgets and thus x - 2 = the number of days it takes Machine Y to produce w widgets. Furthermore, the rate of Machine X is w/x and the rate of Machine Y is w/(x - 2). We are given that they can produce 5w/4 widgets in 3 days. Thus, we have:

3(w/x) + 3[w/(x - 2)] = 5w/4

Dividing both sides by w, we have:

3/x + 3/(x - 2) = 5/4

Multiplying both sides by 4x(x - 2), we have:

12(x - 2) + 12x = 5x(x - 2)

12(x - 2) + 12x = 5x(x - 2)

12x - 24 + 12x = 5x^2 - 10x

5x^2 - 34x + 24 = 0

(5x - 4)(x - 6) = 0

x = 4/5 or x = 6

However, x can’t be 4/5; if it were, y would be negative. Thus, x must be 6. Since it takes Machine X 6 days to produce w widgets, it will take 12 days to produce 2w widgets.

_________________
Scott Woodbury-Stewart Founder and CEO

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11780 messages
Followed by:
1232 members
5254
GMAT Score:
770
Mon Mar 05, 2018 9:12 am
Roland2rule wrote:
Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets.

A. 4
B. 6
C. 8
D. 10
E. 12
Another approach is to assign a nice value to the job (w)

Let's say that w = 12.

GIVEN: Running at their respective constant rates, machine X takes 2 days longer to produce 12 widgets than machine Y
Let t = time for machine Y to produce 12 widgets
So, t+2 = time for machine X to produce 12 widgets

RATE = output/time

So, machine X's RATE = 12 widgets/(t + 2 days) = 12/(t+2) widgets per day
And machine Y's RATE = 12 widgets/(t days) = 12/t widgets per day

The two machines together produce 5w/4 widgets in 3 days
In other words, The two machines together produce 5(12)/4 widgets in 3 days
Or the two machines together produce 15 widgets in 3 days
This means the COMBINED RATE = 5 widgets per day

So, we can write: 12/(t+2) + 12/t = 5
Multiply both sides by (t+2)(t) to get: 12t + 12t + 24 = 5(t+2)(t)
Simplify: 24t + 24 = 5t² + 10t
Rearrange: 5t² - 14t - 24 = 0
Factor to get: (5t + 6)(t - 4) = 0
So, EITHER t = -6/5 OR t = 4
Since the time cannot be negative, it must be the case that t = 4

If t = 4, then it takes Machine Y 4 days to produce 12 widgets
And it takes Machine X 6 days to produce 12 widgets

How many days would it take machine X alone to produce 2w widgets?
In other words, how many days would it take machine X alone to produce 24 widgets? (since w = 12)

If it takes Machine X 6 days to produce 12 widgets, then it will take Machine X 12 days to produce 24 widgets

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
14447 messages
Followed by:
1834 members
13060
GMAT Score:
790
Mon Mar 05, 2018 9:22 am
Quote:
Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?

A) 4
B) 6
C) 8
D) 10
E) 12
Let w = 60 widgets, implying that (5/4)w = (5/4)(60) = 75 widgets.
Since X and Y together can produce (5/4)w widgets in 3 days, the combined rate for X and Y = w/t = 75/3 = 25 widgets per day.

We can PLUG IN THE ANSWERS, which represent X's time to produce 2w widgets.
When the correct answer choice is plugged in, the combined rate for X and Y will be 25 widgets per day.

D: 10
Here, X can produce 2w widgets in 10 days.
Thus, the time for X to produce w widgets = 5 days.

Since X takes 5 days to produce w=60 widgets, X's rate = w/t = 60/5 = 12 widgets per day.
Since X takes 2 days longer than Y to produce w widgets, Y's time to produce w widgets = 3 days.
Since Y takes 3 days to produce w=60 widgets, Y's rate = w/t = 60/3 = 20 widgets per day.
Combined rate for X and Y = 12+20 = 32 widgets per day.

Here, X and Y are working TOO FAST.
Implication:
X must take LONGER to produce 2w widgets, with the result that X and Y will work more SLOWLY.

_________________
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.
Student Review #1
Student Review #2
Student Review #3

Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

### Top First Responders*

1 GMATGuruNY 93 first replies
2 Brent@GMATPrepNow 39 first replies
3 Jay@ManhattanReview 34 first replies
4 Rich.C@EMPOWERgma... 28 first replies
5 Scott@TargetTestPrep 11 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 GMATGuruNY

The Princeton Review Teacher

138 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

134 posts
3 Scott@TargetTestPrep

Target Test Prep

115 posts
4 Jeff@TargetTestPrep

Target Test Prep

104 posts
5 Max@Math Revolution

Math Revolution

92 posts
See More Top Beat The GMAT Experts