Cameron can paint a room in c hours. Cameron and Mackenzie, working to : Problem Solving (PS)

gmatser1

Joined: 07 Feb 2015

Last visit: 16 Jan 2016

Posts: 45

Own Kudos:

77

Given Kudos: 28

Posts: 45

Kudos: 77

06 Sep 2015, 15:06

Kudos

Bookmarks

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:

Show Spoiler

E

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.

EMPOWERgmatRichC

GMAT Club Legend

Joined: 19 Dec 2014

Last visit: 31 Dec 2023

Posts: 21,807

Own Kudos:

12,053

Given Kudos: 450

Status:GMAT Assassin/Co-Founder

Affiliations: EMPOWERgmat

Location: United States (CA)

GMAT 1: 800 Q51 V49 Verified score

GRE 1: Q170 V170

Expert reply

GMAT 1: 800 Q51 V49 Verified score

GRE 1: Q170 V170

Posts: 21,807

Kudos: 12,053

06 Sep 2015, 19:12

Kudos

Bookmarks

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

goldfinchmonster

Joined: 13 Apr 2015

Last visit: 13 Jan 2020

Posts: 60

Own Kudos:

73

Given Kudos: 325

Concentration: General Management, Strategy

Schools: Jenkins FT'18 (S) Desautels '18 Iowa State '18 DeGroote (II) UConn FT "18 Alberta'18 Haskayne(Calgary)

GMAT 1: 620 Q47 V28 Verified score

GPA: 3.25

WE:Project Management (Energy)

Schools: Jenkins FT'18 (S) Desautels '18 Iowa State '18 DeGroote (II) UConn FT "18 Alberta'18 Haskayne(Calgary)

GMAT 1: 620 Q47 V28 Verified score

Posts: 60

Kudos: 73

06 Sep 2015, 19:45

Kudos

Bookmarks

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.

KarishmaB

Tutor

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

Posts: 15,537

Kudos: 70,186

[3]

06 Sep 2015, 21:15

3

Kudos

Bookmarks

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

Show Spoiler

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).

gmatser1

Joined: 07 Feb 2015

Last visit: 16 Jan 2016

Posts: 45

Own Kudos:

77

Given Kudos: 28

Posts: 45

Kudos: 77

11 Sep 2015, 22:34

Kudos

Bookmarks

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.

KarishmaB

Tutor

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

Posts: 15,537

Kudos: 70,186

[2]

12 Sep 2015, 02:12

2

Kudos

Bookmarks

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 = \(\frac{AB}{(A + B)}\)

ashutoshsh

Joined: 07 Mar 2016

Last visit: 07 Feb 2017

Posts: 53

Own Kudos:

169

Given Kudos: 163

Posts: 53

Kudos: 169

25 Mar 2016, 00:49

Kudos

Bookmarks

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

gps5441

Joined: 04 May 2014

Last visit: 03 Feb 2018

Posts: 109

Own Kudos:

74

Given Kudos: 126

Location: India

WE:Sales (Mutual Funds and Brokerage)

Posts: 109

Kudos: 74

27 Mar 2016, 10:34

Kudos

Bookmarks

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

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 Verified score

GMAT 2: 750 Q48 V44 Verified score

GPA: 3.92

Products:

Schools: CBS '20 (A)

GMAT 2: 750 Q48 V44 Verified score

Posts: 34

Kudos: 43

[2]

02 Feb 2017, 04:18

2

Kudos

Bookmarks

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)=\(\frac{1}{(1/d-1/c)}=\frac{1}{(c-d/cd)}=\frac{cd}{c-d}\)

JeffTargetTestPrep

Target Test Prep Representative

Joined: 04 Mar 2011

Last visit: 05 Jan 2024

Posts: 3,023

Own Kudos:

7,201

Given Kudos: 1,646

Status:Head GMAT Instructor

Affiliations: Target Test Prep

Expert reply

Posts: 3,023

Kudos: 7,201

08 Feb 2017, 11:30

Kudos

Bookmarks

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

gracie

Joined: 07 Dec 2014

Last visit: 11 Oct 2020

Posts: 1,048

Own Kudos:

1,715

Given Kudos: 27

Posts: 1,048

Kudos: 1,715

08 Feb 2017, 13:54

Kudos

Bookmarks

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

Show Spoiler

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

Archit3110

GMAT Club Legend

Joined: 18 Aug 2017

Last visit: 10 Dec 2024

Posts: 8,116

Own Kudos:

4,493

Given Kudos: 243

Status:You learn more from failure than from success.

Location: India

Concentration: Sustainability, Marketing

GMAT Focus 1: 545 Q79 V79 DI73 Verified score

GPA: 4

WE:Marketing (Energy)

Products:

GMAT Focus 1: 545 Q79 V79 DI73 Verified score

Posts: 8,116

Kudos: 4,493

24 Jun 2019, 11:38

Kudos

Bookmarks

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

Show Spoiler

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

bumpbot

Non-Human User

Joined: 09 Sep 2013

Last visit: 04 Jan 2021

Posts: 35,781

Own Kudos:

929

Posts: 35,781

Kudos: 929

25 May 2022, 15:54

Kudos

Bookmarks

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.

Cameron can paint a room in c hours. Cameron and Mackenzie, working to

Prep Toolkit

My Rewards

GMAT Problem Solving (PS) Questions

Cameron can paint a room in c hours. Cameron and Mackenzie, working to

Prep Toolkit

My Rewards