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## Cameron can paint a room in c hours. Cameron and Mackenzie..

tagged by: AAPL

This topic has 3 expert replies and 0 member replies

### Top Member

AAPL Moderator
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#### Cameron can paint a room in c hours. Cameron and Mackenzie..

Tue Mar 06, 2018 5:25 am
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?

$$A.\ 2d-c$$
$$B.\ \frac{c+d}{cd}$$
$$C.\ \frac{c-d}{cd}$$
$$D.\ \frac{cd}{c+d}$$
$$E.\ \frac{cd}{c-d}$$

The OA is E.

Can I solve it as follow,

Cameron's rate:
$$Cam's\ rate=\frac{1}{c}$$
Cameron and Mackenzie's rate when working together:
$$Combined\ rate=\frac{1}{d}$$
Mackenzie's rate:
$$Mack's\ rate=\frac{1}{d}-\frac{1}{c}$$
Finally, Mackenzie's time:
$$T(Mackenzie)=\frac{1}{\frac{1}{d}-\frac{1}{c}}=\frac{1}{\frac{c-d}{cd}}=\frac{cd}{c-d}$$
Is there a strategic approach to this question? Can any experts help, please?

### GMAT/MBA Expert

mbawisdom Senior | Next Rank: 100 Posts
Joined
16 Dec 2014
Posted:
94 messages
Followed by:
4 members
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GMAT Score:
770
Tue Mar 06, 2018 5:54 am
AAPL wrote:
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?

$$A.\ 2d-c$$
$$B.\ \frac{c+d}{cd}$$
$$C.\ \frac{c-d}{cd}$$
$$D.\ \frac{cd}{c+d}$$
$$E.\ \frac{cd}{c-d}$$

The OA is E.

Can I solve it as follow,

Cameron's rate:
$$Cam's\ rate=\frac{1}{c}$$
Cameron and Mackenzie's rate when working together:
$$Combined\ rate=\frac{1}{d}$$
Mackenzie's rate:
$$Mack's\ rate=\frac{1}{d}-\frac{1}{c}$$
Finally, Mackenzie's time:
$$T(Mackenzie)=\frac{1}{\frac{1}{d}-\frac{1}{c}}=\frac{1}{\frac{c-d}{cd}}=\frac{cd}{c-d}$$
Is there a strategic approach to this question? Can any experts help, please?
I like the way you approached it. In long form I would solve it as follows:

Rate = Work/Time

(1) Rc = 1/c
(2) Rc + Rd = 1/d
(3) Rd = 1/T

Put (1) and (3) into 2:
1/c + 1/T = 1/d
1/T = 1/d - 1/c
1/T = (c - d)/cd
T = cd/(c-d)

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9599 messages
Followed by:
482 members
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GMAT Score:
800
Tue Mar 06, 2018 6:06 pm
Hi AAPL,

We're told that Cameron can paint a room in C hours and Cameron and Mackenzie, working TOGETHER, can paint the room in D hours. We're asked, in terms of C and D, for how long (in hours) would it take Mackenzie, working alone, to paint the room.

This is an example of a "Work Formula" question - when you have two entities working together on a task, you can use the following formula to determine how long it will take the two entities to complete the task:

(X)(Y)/(X+Y) = time to complete the task (where X and Y are the two times it takes the individuals to complete the task when working alone). We can use this formula - and TEST VALUES - to get the correct answer.

IF...
Cameron takes 3 hours to paint the room and
Mackenzie takes 6 hours to paint the room, then...
it would take (3)(6)/(3+6) = 18/9 = 2 hours for the two of them to paint the room together.

Thus, we're looking for an answer that equals 6 when we plug C=3 and D=2 into it. There's only one answer that matches...

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

_________________
Contact Rich at Rich.C@empowergmat.com

### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
Joined
09 Apr 2015
Posted:
1201 messages
Followed by:
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Thu Mar 08, 2018 4:34 pm
AAPL wrote:
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, Cameron’s rate 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 by herself, 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

_________________
Jeffrey Miller Head of GMAT Instruction

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