It is currently 24 Jun 2017, 09:13

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Running at their respective constant rates, machine X takes

Author Message
Manager
Joined: 16 Oct 2008
Posts: 54
Running at their respective constant rates, machine X takes [#permalink]

### Show Tags

30 Oct 2008, 00:54
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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 5/4 w 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
Intern
Joined: 30 Oct 2008
Posts: 30

### Show Tags

30 Oct 2008, 08:08
1
KUDOS
E.

Let t be number of days.
Rate of Y = w/t
Rate of X = w/(t+2)

When they work together, the number of widgets produced is (combined rate)*time_taken
(X+Y)*3 = 5w/4

substituting X and Y with their rate
w/(t+2) + w/t = 5w/4

Simplifying above equation...
5(t^2) - 12t - 24 = 0

Solving above equation you will get
t = 4

So the time taken to produce 2w widgets by X is 12.

Note:
Two solutions of quadratic equation of form
a(x^2) + bx + c = 0, where a, b and c are constants,are

x = (-b + sqrt(b^2 -4ac))/2a
x = (-b - sqrt(b^2 - 4ac))/2a
Manager
Joined: 16 Oct 2008
Posts: 54

### Show Tags

30 Oct 2008, 20:46
1
KUDOS
OA is E

Tnx a lot
Manager
Joined: 23 Aug 2008
Posts: 63

### Show Tags

04 Nov 2008, 09:50
@mbajingle
Thanks for the detailed solution - I always get confused by rate of work questions. Kudos.
Manager
Joined: 24 Sep 2008
Posts: 189
Schools: MIT / INSEAD / IIM - ABC

### Show Tags

05 Nov 2008, 02:43
mbajingle wrote:
E.

Let t be number of days.
Rate of Y = w/t
Rate of X = w/(t+2)

When they work together, the number of widgets produced is (combined rate)*time_taken
(X+Y)*3 = 5w/4

substituting X and Y with their rate
w/(t+2) + w/t = 5w/4

Simplifying above equation...
5(t^2) - 12t - 24 = 0

Solving above equation you will get
t = 4

So the time taken to produce 2w widgets by X is 12.

Note:
Two solutions of quadratic equation of form
a(x^2) + bx + c = 0, where a, b and c are constants,are

x = (-b + sqrt(b^2 -4ac))/2a
x = (-b - sqrt(b^2 - 4ac))/2a

GOOD goin man........great explanation...thanks!
Manager
Joined: 30 Sep 2008
Posts: 111

### Show Tags

05 Nov 2008, 03:03

@GODSPEED:

Check this

When they work together, the number of widgets produced is (combined rate)*time_taken
(X+Y)*3 = 5w/4

substituting X and Y with their rate
(w/(t+2) + w/t)*3 = 5w/4

and also, t is a number of days for Y
Manager
Joined: 24 Sep 2008
Posts: 189
Schools: MIT / INSEAD / IIM - ABC

### Show Tags

05 Nov 2008, 03:16
lylya4 wrote:

@GODSPEED:

Check this

When they work together, the number of widgets produced is (combined rate)*time_taken
(X+Y)*3 = 5w/4

substituting X and Y with their rate
(w/(t+2) + w/t)*3 = 5w/4

and also, t is a number of days for Y

Didn't get the point man???....you got the same equation as @mbajingle....i think he missed out on 3....rest remains the same

Anyways, thanks for this!
Manager
Joined: 30 Sep 2008
Posts: 111

### Show Tags

05 Nov 2008, 03:20
GODSPEED wrote:
lylya4 wrote:

@GODSPEED:

Check this

When they work together, the number of widgets produced is (combined rate)*time_taken
(X+Y)*3 = 5w/4

substituting X and Y with their rate
(w/(t+2) + w/t)*3 = 5w/4

and also, t is a number of days for Y

Didn't get the point man???....you got the same equation as @mbajingle....i think he missed out on 3....rest remains the same

Anyways, thanks for this!

The equation is his, I just quoted to show he missed 3, that will give the incorrect calculation and the other thing is that t is for Y, so after find out t, he will need to add it by 2.
Re: Combine work Q   [#permalink] 05 Nov 2008, 03:20
Display posts from previous: Sort by