It is currently 18 Nov 2017, 01:54

### 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

# Machine A and Machine B can produce 1 widget in 3 hours work

Author Message
TAGS:

### Hide Tags

Intern
Joined: 15 Oct 2009
Posts: 11

Kudos [?]: 154 [7], given: 11

Machine A and Machine B can produce 1 widget in 3 hours work [#permalink]

### Show Tags

03 Apr 2010, 13:22
7
KUDOS
22
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:15) correct 27% (01:41) wrong based on 975 sessions

### HideShow timer Statistics

Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

A. 1/2
B. 2
C. 3
D. 5
E. 6
[Reveal] Spoiler: OA

Last edited by changhiskhan on 04 Apr 2010, 09:49, edited 1 time in total.

Kudos [?]: 154 [7], given: 11

Manager
Joined: 20 Mar 2010
Posts: 83

Kudos [?]: 110 [10], given: 1

Re: Help with a rate problem. [#permalink]

### Show Tags

03 Apr 2010, 22:49
10
KUDOS
6
This post was
BOOKMARKED
If Machine A takes a hours to produce 1 widget it produces 1/a th of widget every hour
Similarly If Machine B takes b hours to produce 1 widget it produces 1/b th of widget every hour

If Machine A and Machine B work together they can produce 1 widget in 3 hrs . So together they can produce 1/3rd of the widget in an hour

Work done by A in 1 hour + Work done by B in 1 hour = Work done by A and B together in 1 hour

1/a + 1/ b =1/3

If A's speed is doubled time it takes to produce 1 widget on it's own will reduce by 1/2
So 2/a + 1/b = 1/2

1/a =1/2-1/3
=1/6

a = 6 hrs. Answer D
_________________

___________________________________
Please give me kudos if you like my post

Kudos [?]: 110 [10], given: 1

Senior Manager
Status: Yeah well whatever.
Joined: 18 Sep 2009
Posts: 341

Kudos [?]: 79 [2], given: 17

Location: United States
GMAT 1: 660 Q42 V39
GMAT 2: 730 Q48 V42
GPA: 3.49
WE: Analyst (Insurance)
Re: Help with a rate problem. [#permalink]

### Show Tags

03 Apr 2010, 22:52
2
KUDOS
It should be the second D that I think is supposed to be E. I've attached my work in a spreadsheet
Attachments

For GMAT CLUB.xlsx [11.63 KiB]

_________________

He that is in me > he that is in the world. - source 1 John 4:4

Kudos [?]: 79 [2], given: 17

Senior Manager
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 320

Kudos [?]: 894 [5], given: 28

Re: Help with a rate problem. [#permalink]

### Show Tags

07 Jun 2010, 05:28
5
KUDOS
2
This post was
BOOKMARKED
changhiskhan wrote:
Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

a) 1/2
b) 2
c) 3
d) 5
e) 6

Thanks!

the quickest way to solve this problem is to know the following shortcuts ..

If machine A and B work together, then:
1 hour = (A+B)/AB of work done ..... (1)
AB/(A+B) hour = 1 job done ..... (2)

the questions discusses time, so we'll use (1) equation. plug in the values.

(a+b)/ab = 3
(a/2+b)/(a/2*b) = 2 ....... [the speed is doubled so the time is halved]

solve the equations and you'll get a=6 hrs

_________________

press kudos, if you like the explanation, appreciate the effort or encourage people to respond.

Kudos [?]: 894 [5], given: 28

Manager
Status: Last few days....Have pressed the throttle
Joined: 20 Jun 2010
Posts: 67

Kudos [?]: 62 [1], given: 27

WE 1: 6 years - Consulting
Re: Help with a rate problem. [#permalink]

### Show Tags

17 Aug 2010, 19:16
1
KUDOS
My way of doing it:
Check all the times given in Question-3 hr and 2 hr - take LCM = 6; SO 6 is the total units of work to be done.
W=6 units
now , a+b = 6units/3hr= 2u/hr -(I) (work done by a and b together in 1 hr)

with double speed of a:

2a+b=6u/2hr= 3u/hr (II)

by I & II a=1 units per hour -> so total time taken to complete the full work is 6*1 (6 units * 1 unit per hour) = 6 hours is the answer.

NOTE: This method helps to solve the problem orally !
_________________

Consider giving Kudos if my post helps in some way

Kudos [?]: 62 [1], given: 27

Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 404

Kudos [?]: 259 [0], given: 50

Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: Help with a rate problem. [#permalink]

### Show Tags

17 Aug 2010, 19:30
changhiskhan wrote:
Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

a) 1/2
b) 2
c) 3
d) 5
e) 6

Thanks!

My attempt:

Given rate at which A & B works at normal pace to complete 1 widget is (1/3).

Hence A's rate = B's rate = half of (1/3).

Hence A's rate is (1/6), so to complete 1 widget A requires 6 hours.

Any thoughts ?????
_________________

Support GMAT Club by putting a GMAT Club badge on your blog

Kudos [?]: 259 [0], given: 50

Senior Manager
Status: Yeah well whatever.
Joined: 18 Sep 2009
Posts: 341

Kudos [?]: 79 [0], given: 17

Location: United States
GMAT 1: 660 Q42 V39
GMAT 2: 730 Q48 V42
GPA: 3.49
WE: Analyst (Insurance)
Re: Help with a rate problem. [#permalink]

### Show Tags

17 Aug 2010, 19:34
lol I put it in a spreadsheet... what a nerd I am. I forgot that I did that.
_________________

He that is in me > he that is in the world. - source 1 John 4:4

Kudos [?]: 79 [0], given: 17

Senior Manager
Joined: 23 May 2010
Posts: 416

Kudos [?]: 144 [2], given: 112

Re: Help with a rate problem. [#permalink]

### Show Tags

29 Aug 2010, 10:30
2
KUDOS
ezhilkumarank wrote:
changhiskhan wrote:
Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

a) 1/2
b) 2
c) 3
d) 5
e) 6

Thanks!

My attempt:

Given rate at which A & B works at normal pace to complete 1 widget is (1/3).

Hence A's rate = B's rate = half of (1/3).

Hence A's rate is (1/6), so to complete 1 widget A requires 6 hours.

Any thoughts ?????

hi
I dont think it wil give u a correct result everytime ..
I dont think 1/6+1/6= 1/3 ( where in A and B rate of work is same )

however these speeds may vary ad yet the totalmay be 1/3....not sure If i have explained u??

Kudos [?]: 144 [2], given: 112

Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 404

Kudos [?]: 259 [1], given: 50

Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: Help with a rate problem. [#permalink]

### Show Tags

29 Aug 2010, 19:36
1
KUDOS
gauravnagpal wrote:
ezhilkumarank wrote:
changhiskhan wrote:
Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

a) 1/2
b) 2
c) 3
d) 5
e) 6

Thanks!

My attempt:

Given rate at which A & B works at normal pace to complete 1 widget is (1/3).

Hence A's rate = B's rate = half of (1/3).

Hence A's rate is (1/6), so to complete 1 widget A requires 6 hours.

Any thoughts ?????

hi
I dont think it wil give u a correct result everytime ..
I dont think 1/6+1/6= 1/3 ( where in A and B rate of work is same )

however these speeds may vary ad yet the totalmay be 1/3....not sure If i have explained u??

I understand your point. A's rate could be 1/12 and B's rate be 1/4 but still working together they could end up with a combined rate of 1/3.

I believe the key mistake of my approach is not understanding the key part of the question -- "[highlight]working together at their respective constant rates[/highlight]"

Thanks for pointing this and correcting me. +1 from me.
_________________

Support GMAT Club by putting a GMAT Club badge on your blog

Kudos [?]: 259 [1], given: 50

SVP
Joined: 30 Apr 2008
Posts: 1863

Kudos [?]: 623 [0], given: 32

Location: Oklahoma City
Schools: Hard Knocks
Re: Help with a rate problem. [#permalink]

### Show Tags

29 Aug 2010, 20:41
I just wanted to point out that answers A, B, and C don't even make sense.
_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a.

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 623 [0], given: 32

Manager
Joined: 02 Nov 2009
Posts: 137

Kudos [?]: 206 [0], given: 97

Re: Help with a rate problem. [#permalink]

### Show Tags

07 Sep 2012, 21:15
1
This post was
BOOKMARKED
Bunuel

Kudos [?]: 206 [0], given: 97

Director
Joined: 22 Mar 2011
Posts: 610

Kudos [?]: 1072 [4], given: 43

WE: Science (Education)
Re: Help with a rate problem. [#permalink]

### Show Tags

08 Sep 2012, 00:14
4
KUDOS
1
This post was
BOOKMARKED
venmic wrote:
Bunuel

crack700 already gave you the correct answer (6 is correct, so the answer is E and not D).

The two equations are:

$$\frac{1}{A}+\frac{1}{B}=\frac{1}{3}$$

$$\frac{2}{A}+\frac{1}{B}=\frac{1}{2}$$

Subtract the first equation from the second. You obtain $$\frac{1}{A}=\frac{1}{6}$$ , so $$A=6.$$

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Kudos [?]: 1072 [4], given: 43

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132539 [9], given: 12324

Re: Help with a rate problem. [#permalink]

### Show Tags

08 Sep 2012, 02:20
9
KUDOS
Expert's post
11
This post was
BOOKMARKED
venmic wrote:
Bunuel

Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

A. 1/2
B. 2
C. 3
D. 5
E. 6

Say the rate of machine A is $$a$$ widgets per hour and the rate of machine B is $$b$$ widgets per hour. Since working together they can produce 1 widget in 3 hours, then their combined rate is $$\frac{1}{3}$$ widgets per hour. So, we have that:

$$a+b=\frac{1}{3}$$.

Similarly the second equation would be:

$$2a+b=\frac{1}{2}$$.

Subtract the first equation from the second: $$a=\frac{1}{6}$$ widgets per hour. So, machine A needs 6 hours to produce 1 widget.

_________________

Kudos [?]: 132539 [9], given: 12324

Senior Manager
Joined: 13 Aug 2012
Posts: 458

Kudos [?]: 556 [0], given: 11

Concentration: Marketing, Finance
GPA: 3.23
Re: Machine A and Machine B can produce 1 widget in 3 hours work [#permalink]

### Show Tags

15 Nov 2012, 05:45
$$\frac{1}{A}+\frac{1}{B}=\frac{1}{3}$$
$$\frac{2}{A}+\frac{1}{B}=\frac{1}{2}$$

Combine the two eq:

$$\frac{2}{A}-\frac{1}{A}=\frac{1}{2}-\frac{1}{3}$$
$$\frac{1}{A}=\frac{1}{6}$$

$$t=6$$
_________________

Impossible is nothing to God.

Kudos [?]: 556 [0], given: 11

Non-Human User
Joined: 09 Sep 2013
Posts: 15714

Kudos [?]: 281 [0], given: 0

Re: Machine A and Machine B can produce 1 widget in 3 hours work [#permalink]

### Show Tags

07 May 2014, 07:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 281 [0], given: 0

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10111

Kudos [?]: 3505 [1], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: Machine A and Machine B can produce 1 widget in 3 hours work [#permalink]

### Show Tags

19 Mar 2015, 18:03
1
KUDOS
Expert's post
Hi All,

This question is a bit more complex than a typical Work question, but you can still use the Work Formula to solve it.

Work = (A)(B)/(A+B) where A and B are the speeds of the two individual machines

From the prompt, we know that Machine A and Machine B, working together, can produce 1 widget in 3 hours. This is the same as saying "it takes 3 hours to complete 1 job."

Using the Work Formula, we have....

(A)(B)/(A+B) = 3

AB = 3A + 3B

Next, we're told that if Machine A's speed were DOUBLED, then the two machines would need 2 hours to produce 1 widget. Mathematically, doubling Machine A's speed means that we have to refer to it as A/2 (if the original speed is 1 widget every 10 hours, then DOUBLING that speed means 1 widget every 5 hours.....thus A becomes A/2).

Using the Work Formula, we have....

(A/2)(B)/(A/2 + B) = 2

(AB)/2 = A + 2B
AB = 2A + 4B

Now we have two variables and two equations. Both equations are set equal to "AB", so we have....

3A + 3B = 2A + 4B
A = B

This tells us that the original speeds of both machines are the SAME. Going back to the original formula, we can substitute in the value of "B" which gives us....

AB = 3A + 3B

A(A) = 3A + 3(A)

A^2 = 6A

A^2 - 6A = 0
A(A-6) = 0

Since a machine cannot have a rate of 0, Machine A's rate must be 1 unit per 6 hours.

[Reveal] Spoiler:
E

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3505 [1], given: 173

Current Student
Joined: 09 Aug 2015
Posts: 94

Kudos [?]: 30 [0], given: 7

GMAT 1: 770 Q51 V44
GPA: 2.3
Re: Machine A and Machine B can produce 1 widget in 3 hours work [#permalink]

### Show Tags

10 Aug 2015, 17:46
Hi guys, here is my solution, please take a look and let me know if this is a correct way to think:

Let A,B be rates of machines A,B

3 hours*A + 3 hours*B = 1 widget
or
3A + 3B = 1

2 hours*2*A + 2 hours*B = 1 widget
or
4A + 2B = 1

Subtract the two equations:

A-B = 0 => A = B

Plug back in:

3A + 3A = 1, A = 1/6

Therefore A takes 6 hours working at its rate of 1/6 to make 1 widget

Kudos [?]: 30 [0], given: 7

Re: Machine A and Machine B can produce 1 widget in 3 hours work   [#permalink] 10 Aug 2015, 17:46
Display posts from previous: Sort by