Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 06:16 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Kyra and Sage, working together can paint a room in 5 hours. If Melora

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56307
Kyra and Sage, working together can paint a room in 5 hours. If Melora  [#permalink]

### Show Tags

1
2 00:00

Difficulty:   5% (low)

Question Stats: 95% (01:11) correct 5% (02:17) wrong based on 103 sessions

### HideShow timer Statistics Kyra and Sage, working together can paint a room in 5 hours. If Melora helps Kyra and Sage paint the room, the three of them can paint the room in 4 hours. What amount of time (in hours) would it take Melora, working alone, to paint the room?

(A) 6
(B) 8
(C) 10
(D) 15
(E) 20

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56307
Re: Kyra and Sage, working together can paint a room in 5 hours. If Melora  [#permalink]

### Show Tags

Bunuel wrote:
Kyra and Sage, working together can paint a room in 5 hours. If Melora helps Kyra and Sage paint the room, the three of them can paint the room in 4 hours. What amount of time (in hours) would it take Melora, working alone, to paint the room?

(A) 6
(B) 8
(C) 10
(D) 15
(E) 20

17. Work/Rate Problems

On other subjects:
ALL YOU NEED FOR QUANT ! ! !
_________________
Senior PS Moderator D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 751
GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: Kyra and Sage, working together can paint a room in 5 hours. If Melora  [#permalink]

### Show Tags

1
Bunuel wrote:
Kyra and Sage, working together can paint a room in 5 hours. If Melora helps Kyra and Sage paint the room, the three of them can paint the room in 4 hours. What amount of time (in hours) would it take Melora, working alone, to paint the room?

(A) 6
(B) 8
(C) 10
(D) 15
(E) 20

Rate of painting room for K + S = 1/5 ( how much part of the room they can paint in one hour )

When M is working with K & S -> New rate is 1/4 ( as they take 4 hrs to paint room , they paint 1/4th room in one hour)

Let M alone finish paint job in x hours. So her rate is 1/x.

So Rate of K&S + Rate of M = Rate of K&S&M together.

We have...

$$1/5 + 1/x = 1/4$$
$$1/x = 1/4 - 1/5$$
$$1/x = (5-4)/20$$
$$x = 20$$
Hence E.

Please give Kudos if you liked the explanation...
_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Board of Directors P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4512
Location: India
GPA: 3.5
Re: Kyra and Sage, working together can paint a room in 5 hours. If Melora  [#permalink]

### Show Tags

Bunuel wrote:
Kyra and Sage, working together can paint a room in 5 hours. If Melora helps Kyra and Sage paint the room, the three of them can paint the room in 4 hours. What amount of time (in hours) would it take Melora, working alone, to paint the room?

(A) 6
(B) 8
(C) 10
(D) 15
(E) 20

Let the total work be 20 units

So, Efficiency of Kyra and Sage is 4 units
And, Efficiency of Melora , Kyra and Sage is 5 units

So, We have ( k + s ) + m = 5 ; 4 + s = 5

So, Efficiency of m is 1 , Thus time required by Melora to paint the room is 20 Hours, Answer must be (E)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager  B
Joined: 28 Jan 2018
Posts: 51
Location: Netherlands
Concentration: Finance
GMAT 1: 710 Q50 V36 GPA: 3
Kyra and Sage, working together can paint a room in 5 hours. If Melora  [#permalink]

### Show Tags

Bunuel wrote:
Kyra and Sage, working together can paint a room in 5 hours. If Melora helps Kyra and Sage paint the room, the three of them can paint the room in 4 hours. What amount of time (in hours) would it take Melora, working alone, to paint the room?

(A) 6
(B) 8
(C) 10
(D) 15
(E) 20

In 1 hour, Kyra and Sage can paint 1/5 of the room
In 1 hour, Kyra, Sage and Melora can paint 1/4 of the room

Therefore, in 1 hour, Melora can paint 1/4 - 1/5 = 1/20 of the room

Therefore Melora needs 20 hours to paint the room => Answer (E)
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3094
Kyra and Sage, working together can paint a room in 5 hours. If Melora  [#permalink]

### Show Tags

Bunuel wrote:
Kyra and Sage, working together can paint a room in 5 hours. If Melora helps Kyra and Sage paint the room, the three of them can paint the room in 4 hours. What amount of time (in hours) would it take Melora, working alone, to paint the room?

(A) 6
(B) 8
(C) 10
(D) 15
(E) 20

The combined rate of two persons is given. When the third person, Melora, joins, the equation is simple.

1) Combined rate of Sage and Kyra = $$\frac{1}{5}$$
Substitute that rate in the next step

2) Combined rate of Sage, Kyra, and Melora: Together all three can paint the room in 4 hours:
$$(\frac{1}{S}+\frac{1}{K})+\frac{1}{M}=\frac{1}{4}$$, that is,
$$\frac{1}{5}+\frac{1}{M}=\frac{1}{4}$$

3) Melora's rate, working alone*:
$$\frac{1}{M}=(\frac{1}{4}-\frac{1}{5}) = (\frac{(5-4)}{20})=\frac{1}{20}$$

4) M's time?
Work is 1 (room). Rate is inversely proportional to time. Flip the rate fraction: $$\frac{1room}{20hrs} -> \frac{20hrs}{1room}$$

Melora takes 20 hours to paint the room alone.

*Shortcuts
Rates:$$\frac{1}{A}-\frac{1}{B} =\frac{(B-A)}{AB}$$
Use LCM to see proof.
For added rates, the shortcut is $$\frac{1}{A}+\frac{1}{B}=\frac{(A+B)}{AB}$$

Inverting (flipping) the rate fraction to get time
$$W = 1$$ room, $$r$$
$$R * T = W$$, so $$T = \frac{W}{R}$$
$$T=\frac{1r}{\frac{1r}{20hrs}}= (1r * \frac{20hrs}{1r}) = 20 hrs$$

_________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.

-- Take another look. Take a look around. These are the moments you can't pass by.
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 2943
Kyra and Sage, working together can paint a room in 5 hours. If Melora  [#permalink]

### Show Tags

Solution

Let the total amount of work done to paint the room is $$LCM (5,4) = 20$$ units.

Kyra and Sage, working together can paint a room in $$5$$ hours.
o Thus, Kyra and Sage complete $$4$$ units of work in $$1$$ hour.
o $$K+S=4$$----------------------$$(1)$$

If Melora helps Kyra and Sage paint the room, the three of them can paint the room in $$4$$ hours.
o Thus, Kyra, Sage, and Melora complete $$5$$ units of work in $$1$$ hour.
o $$K+S+M=5$$-------------------$$(2)$$

By subtracting equation $$(1)$$ from equation $$(2)$$, we get:
• $$M=1$$ unit, OR, $$M$$ completes $$1$$ unit of work in $$1$$ hour.

• Thus, to complete $$20$$units of work Melora will take $$\frac{20}{1}$$=$$20$$ hours.

_________________
VP  P
Joined: 07 Dec 2014
Posts: 1210
Kyra and Sage, working together can paint a room in 5 hours. If Melora  [#permalink]

### Show Tags

Bunuel wrote:
Kyra and Sage, working together can paint a room in 5 hours. If Melora helps Kyra and Sage paint the room, the three of them can paint the room in 4 hours. What amount of time (in hours) would it take Melora, working alone, to paint the room?

(A) 6
(B) 8
(C) 10
(D) 15
(E) 20

K and S paint 1/5 of the room in 1 hour
M saves them 1 hour by painting 1/5 of the room in 4 hours
4/(1/5)=20 hours for M to paint room alone
E
Intern  B
Joined: 31 Jan 2017
Posts: 9
Kyra and Sage, working together can paint a room in 5 hours. If Melora  [#permalink]

### Show Tags

Bunuel wrote:
Kyra and Sage, working together can paint a room in 5 hours. If Melora helps Kyra and Sage paint the room, the three of them can paint the room in 4 hours. What amount of time (in hours) would it take Melora, working alone, to paint the room?

(A) 6
(B) 8
(C) 10
(D) 15
(E) 20

Remember: Rate * Time = Work
K = Kyra | S = Sage | M = Melora

(K+S) * 5 = 1 --> (K + S) working together at their own rate took 5 hours to paint 1 room.
This means the rate at which (K + S) work is (1/5).

(M+K+S) * 4 = 1 --> (M + K + S) working together at their own rate took 4 hours to paint 1 room.
This means the rate at which (M + K + S) work is (1/4).

Now we need to figure out at what rate Melora (M) works at:
(M + K + S) = (1/4) --> This is the rate at which when (M + K + S) work together.
(M) + (1/5) = (1/4) --> We already know that (K + S) = 1/5 since this is the rate at which they work together.
M = (1/4) - (1/5)
M = (1/20) --> This is the rate at which Melora (M) works alone.

Now to solve for how long it will take Melora to paint 1 room:
R * T = W --> Our standard rate formula
(1/20) * T = 1 --> Plug in the rate for which Melora works (1/20) and solve for T (time)
T = 20

Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2822
Re: Kyra and Sage, working together can paint a room in 5 hours. If Melora  [#permalink]

### Show Tags

Bunuel wrote:
Kyra and Sage, working together can paint a room in 5 hours. If Melora helps Kyra and Sage paint the room, the three of them can paint the room in 4 hours. What amount of time (in hours) would it take Melora, working alone, to paint the room?

(A) 6
(B) 8
(C) 10
(D) 15
(E) 20

We can let K, S, and M = the time it takes Kyra, Sage, and Melora to paint the room respectively and create the equations:

1/K + 1/S = 1/5

And

1/M + 1/K + 1/S = 1/4

Subtracting the first equation from the second we have:

1/M = 1/4 - 1/5

1/M = 5/20 - 4/20 = 1/20

So it would take Melora 20 hours to paint the room.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: Kyra and Sage, working together can paint a room in 5 hours. If Melora   [#permalink] 05 Apr 2018, 11:05
Display posts from previous: Sort by

# Kyra and Sage, working together can paint a room in 5 hours. If Melora  