Last visit was: 11 Dec 2024, 00:26 It is currently 11 Dec 2024, 00:26
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
avatar
gmatser1
Joined: 07 Feb 2015
Last visit: 16 Jan 2016
Posts: 45
Own Kudos:
77
 [8]
Given Kudos: 28
Posts: 45
Kudos: 77
 [8]
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
avatar
gmatser1
Joined: 07 Feb 2015
Last visit: 16 Jan 2016
Posts: 45
Own Kudos:
Given Kudos: 28
Posts: 45
Kudos: 77
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
EMPOWERgmatRichC
User avatar
GMAT Club Legend
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,807
Own Kudos:
12,053
 [3]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,807
Kudos: 12,053
 [3]
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
avatar
gmatser1
Joined: 07 Feb 2015
Last visit: 16 Jan 2016
Posts: 45
Own Kudos:
Given Kudos: 28
Posts: 45
Kudos: 77
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EMPOWERgmatRichC
Hi gmatser1,

This prompt can be solved by TESTing VALUES and using the Work Formula:

Work = (A)(B)/(A+B) where A and B are the individual times that it takes to complete the 'job'

Here, we're told that one person can paint a room in C hours and that two people (when WORKING TOGETHER) can paint the room in D hours. We're asked for the individual amount of time that it would take the second person to paint the room when working along.

IF...
the 1st person can paint the room in 3 hours
the 2nd person can paint the room in 6 hours
Combined, it would take (3)(6)/(3+6) = 18/9 = 2 hours to paint the room when working together

Using the above example, we can TEST VALUES....
C = 3
D = 2

And we're looking for an answer that equals 6....There's only one answer that fits....

Final Answer:
GMAT assassins aren't born, they're made,
Rich

Rich,

Appreciate the response! However I still don't understand how the Work = (A)(B)/(A+B) combined rate equation is derived.

I understand that combined rates can be added or subtracted to determine the combined or individual rate, (i.e, Combined Rate = R1 + R2) and can be used in the overall rate formula (W = CR(T)) but not sure how that relates to time.
User avatar
EMPOWERgmatRichC
User avatar
GMAT Club Legend
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,807
Own Kudos:
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,807
Kudos: 12,053
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi gmatser1,

It sounds like you're asking about "why" the Work Formula provides the answer that it does. While I could explain the deeper math involved, that knowledge is really unnecessary. The Work Formula IS a formula that you can use to answer this type of question, whether you understand why it works or not. In that same way, do you need to know why the Pythagorean Theorem 'works' to answer 'right-triangle' questions? Or how the Combination Formula eliminates all of the duplicate entries?

I respect any 'quest' for knowledge that you might have, but if it's knowledge that isn't necessary to score at a high level on the GMAT, then I won't spend your valuable time on it.

GMAT assassins aren't born, they're made,
Rich
User avatar
goldfinchmonster
Joined: 13 Apr 2015
Last visit: 13 Jan 2020
Posts: 60
Own Kudos:
Given Kudos: 325
Concentration: General Management, Strategy
GMAT 1: 620 Q47 V28
GPA: 3.25
WE:Project Management (Energy)
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Cam's Time = C , Mack's Time = M ( Assume ) , Combined Time = D ( Given )

Let Work be = X

Then,

Cam's Speed = X / C, Mack's Speed = X / M.

Combined time should be ( D ) = Total Work/Their speed together( Addition of their speeds ).

i.e x / (x/c) + (x/m) = D

Solving the equation, M = dc/( c-d ).

Ans E.
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 10 Dec 2024
Posts: 15,537
Own Kudos:
70,186
 [3]
Given Kudos: 449
Location: Pune, India
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 15,537
Kudos: 70,186
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatser1
Cameron can paint a room in c hours. Cameron and Mackenzie, working together, can paint the room in d hours. In terms of c and d, how long in hours would it take Mackenzie, working alone, to paint the room?

(A) 2d - c

(B) \(\frac{c+d}{cd}\)

(C) \(\frac{c-d}{cd}\)

(D) \(\frac{cd}{c+d}\)

(E) \(\frac{cd}{c-d}\)

Explanation: While it may be easier to work with actual numbers, this question is an explicit test of your knowledge of the work formula. If you know the time it takes for two individuals to do a job, you can plug those times into the equation \(\frac{xy}{x+y}\) to get the time it would take them, combined. Thus, plugging c in for x and setting the whole thing equal to d:

\(\frac{cy}{c + y}= d\)

\(cy= d(c + y)\)

\(cy = dc + dy\)

\(cy - dy = dc\)

\(y = \frac{dc}{c-d}\)

which is equivalent to \(\frac{cd}{c-d}\), choice (E).

Source: GMAT HACKS 1800 - Guide 1 - Rates, Ratios & Percents

Assume simple values.

If Cameron takes 2 hrs alone and Mackenzie takes 2 hrs alone, they both will take 1 hr working together. (If rate is same, for 2 people, time taken will be halved)
So put c = 2, d = 1.
The only option that gives you 2 (time taken by Mackenzie alone) is option (E).
avatar
gmatser1
Joined: 07 Feb 2015
Last visit: 16 Jan 2016
Posts: 45
Own Kudos:
Given Kudos: 28
Posts: 45
Kudos: 77
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EMPOWERgmatRichC
Hi gmatser1,

It sounds like you're asking about "why" the Work Formula provides the answer that it does. While I could explain the deeper math involved, that knowledge is really unnecessary. The Work Formula IS a formula that you can use to answer this type of question, whether you understand why it works or not. In that same way, do you need to know why the Pythagorean Theorem 'works' to answer 'right-triangle' questions? Or how the Combination Formula eliminates all of the duplicate entries?

I respect any 'quest' for knowledge that you might have, but if it's knowledge that isn't necessary to score at a high level on the GMAT, then I won't spend your valuable time on it.

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

Rich,

Thanks. So Work = (A)(B)/(A+B) is just another thing I have to memorize? Similar to how I just "know" Combined rate = R1 + R2?

Thanks so much for you help.
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 10 Dec 2024
Posts: 15,537
Own Kudos:
70,186
 [2]
Given Kudos: 449
Location: Pune, India
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 15,537
Kudos: 70,186
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatser1
I still don't understand how the Work = (A)(B)/(A+B) combined rate equation is derived.

I understand that combined rates can be added or subtracted to determine the combined or individual rate, (i.e, Combined Rate = R1 + R2) and can be used in the overall rate formula (W = CR(T)) but not sure how that relates to time.

AB/(A+B) is the same thing as Combined Rate = R1 + R2.

Note that A and B is time taken in hours.

\(Rate = \frac{1}{Time}\) when work done is 1 (usually 1 job such as paint a room) because Work = Rate * Time

Combined Rate = R1 + R2

\(\frac{1}{Time Taken Together} = \frac{1}{A} + \frac{1}{B}\)

Time taken together = \(\frac{AB}{(A + B)}\)
User avatar
ashutoshsh
Joined: 07 Mar 2016
Last visit: 07 Feb 2017
Posts: 53
Own Kudos:
Given Kudos: 163
Posts: 53
Kudos: 169
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given : R(c) = 1/c
R(m) = 1/m (Say M alone can complete the job in 'm' hours)
Given: R(cm) = 1/d
therefor, 1/d = 1/c + 1/m
1/d-1/c=1/m
c-d/(cd) = 1/m ( this is the rate at which M can work)
therefore , Time Taken by M is... 1/Rate ie cd/(c-d) ie option E
User avatar
gps5441
Joined: 04 May 2014
Last visit: 03 Feb 2018
Posts: 109
Own Kudos:
Given Kudos: 126
Location: India
WE:Sales (Mutual Funds and Brokerage)
Posts: 109
Kudos: 74
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Combined rate of work
1/c+1/M=1/d
1/M=1/d-1/c
1/M=c-d/dc
Time=reciprocal of rate=dc/c-d

Posted from my mobile device
User avatar
cavana
Joined: 20 Jan 2017
Last visit: 20 Jun 2018
Posts: 34
Own Kudos:
43
 [2]
Given Kudos: 15
Location: United States (NY)
Schools: CBS '20 (A)
GMAT 1: 610 Q34 V41
GMAT 2: 750 Q48 V44
GPA: 3.92
Products:
Schools: CBS '20 (A)
GMAT 2: 750 Q48 V44
Posts: 34
Kudos: 43
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1) Cameron's rate: \(\frac{1}{c}\)
2) Cameron and Mackenzie's rate when working together: \(\frac{1}{d}\)
3) Mackenzie's rate: \(\frac{1}{d}-\frac{1}{c}\)
4) T(Mackenzie)=\(\frac{1}{(1/d-1/c)}=\frac{1}{(c-d/cd)}=\frac{cd}{c-d}\)
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 3,023
Own Kudos:
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert reply
Posts: 3,023
Kudos: 7,201
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatser1
Cameron can paint a room in c hours. Cameron and Mackenzie, working together, can paint the room in d hours. In terms of c and d, how long in hours would it take Mackenzie, working alone, to paint the room?

(A) 2d - c

(B) \(\frac{c+d}{cd}\)

(C) \(\frac{c-d}{cd}\)

(D) \(\frac{cd}{c+d}\)

(E) \(\frac{cd}{c-d}\)

We are given that Cameron can paint a room in c hours. Since rate = work/time, the rate of Cameron is 1/c. We are also given that, working together, Cameron and Mackenzie can paint the room in d hours. If we let m = the time it takes Mackenzie to paint the room alone, we can create the following equation:

1/c + 1/m = 1/d

We need to determine how long it would take Mackenzie to paint the room, so we need to isolate m.

We can start by multiplying the entire equation by cmd:

md + cd = cm

cd = cm - md

cd = m(c - d)

cd/(c-d) = m

Answer: E
User avatar
gracie
Joined: 07 Dec 2014
Last visit: 11 Oct 2020
Posts: 1,048
Own Kudos:
Given Kudos: 27
Posts: 1,048
Kudos: 1,715
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatser1
Cameron can paint a room in c hours. Cameron and Mackenzie, working together, can paint the room in d hours. In terms of c and d, how long in hours would it take Mackenzie, working alone, to paint the room?

(A) 2d - c

(B) \(\frac{c+d}{cd}\)

(C) \(\frac{c-d}{cd}\)

(D) \(\frac{cd}{c+d}\)

(E) \(\frac{cd}{c-d}\)

Explanation: While it may be easier to work with actual numbers, this question is an explicit test of your knowledge of the work formula. If you know the time it takes for two individuals to do a job, you can plug those times into the equation \(\frac{xy}{x+y}\) to get the time it would take them, combined. Thus, plugging c in for x and setting the whole thing equal to d:

\(\frac{cy}{c + y}= d\)

\(cy= d(c + y)\)

\(cy = dc + dy\)

\(cy - dy = dc\)

\(y = \frac{dc}{c-d}\)

which is equivalent to \(\frac{cd}{c-d}\), choice (E).

Source: GMAT HACKS 1800 - Guide 1 - Rates, Ratios & Percents
1/d-1/c=(c-d)/cd=M's rate
inverting, cd/(c-d)=M's time to paint room alone
E
User avatar
Archit3110
User avatar
GMAT Club Legend
Joined: 18 Aug 2017
Last visit: 10 Dec 2024
Posts: 8,116
Own Kudos:
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy)
Products:
GMAT Focus 1: 545 Q79 V79 DI73
Posts: 8,116
Kudos: 4,493
Kudos
Add Kudos
Bookmarks
Bookmark this Post
given
C= 1/c
and 1/C+1/m=1/d
so
1/m=1/d-1/c
m=\(\frac{cd}{c-d}\)
IMO E


gmatser1
Cameron can paint a room in c hours. Cameron and Mackenzie, working together, can paint the room in d hours. In terms of c and d, how long in hours would it take Mackenzie, working alone, to paint the room?

(A) 2d - c

(B) \(\frac{c+d}{cd}\)

(C) \(\frac{c-d}{cd}\)

(D) \(\frac{cd}{c+d}\)

(E) \(\frac{cd}{c-d}\)

Explanation: While it may be easier to work with actual numbers, this question is an explicit test of your knowledge of the work formula. If you know the time it takes for two individuals to do a job, you can plug those times into the equation \(\frac{xy}{x+y}\) to get the time it would take them, combined. Thus, plugging c in for x and setting the whole thing equal to d:

\(\frac{cy}{c + y}= d\)

\(cy= d(c + y)\)

\(cy = dc + dy\)

\(cy - dy = dc\)

\(y = \frac{dc}{c-d}\)

which is equivalent to \(\frac{cd}{c-d}\), choice (E).

Source: GMAT HACKS 1800 - Guide 1 - Rates, Ratios & Percents
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 35,781
Own Kudos:
Posts: 35,781
Kudos: 929
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderator:
Math Expert
97779 posts