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# Kathleen can paint a room in 3 hours, and Anthony can paint an identic

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Kathleen can paint a room in 3 hours, and Anthony can paint an identic  [#permalink]

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27 Dec 2015, 09:35
00:00

Difficulty:

45% (medium)

Question Stats:

58% (01:08) correct 42% (00:48) wrong based on 276 sessions

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Kathleen can paint a room in 3 hours, and Anthony can paint an identical room in 5 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?

A. 8/15
B. 4/3
C. 15/8
D. 9/4
E. 15/4

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Joined: 15 Feb 2015
Posts: 92
Re: Kathleen can paint a room in 3 hours, and Anthony can paint an identic  [#permalink]

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27 Dec 2015, 10:32
Bunuel wrote:
Kathleen can paint a room in 3 hours, and Anthony can paint an identical room in 5 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?

A. 8/15
B. 4/3
C. 15/8
D. 9/4
E. 15/4

kat---3 hrs---1 room ; so rate is work/time= 1/3

Anthony---5 hrs---1 room ; rate= 1/5

rate of kat and anthony together=1/3+1/5 = 8/15

But we are told that they both paint 2 rooms which are identical.
So; Work is 2 rooms, rate is 8/15,
total time required for both of them together to complete the work = 2/(8/15)= 30/8= 15/4

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Re: Kathleen can paint a room in 3 hours, and Anthony can paint an identic  [#permalink]

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27 Dec 2015, 22:11
Bunuel wrote:
Kathleen can paint a room in 3 hours, and Anthony can paint an identical room in 5 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?

A. 8/15
B. 4/3
C. 15/8
D. 9/4
E. 15/4

(1/3 + 1/5)t=2
t=15/4

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Re: Kathleen can paint a room in 3 hours, and Anthony can paint an identic  [#permalink]

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28 Dec 2015, 23:18
Hi All,

This is a standard Work Formula question (2 or more 'entities' that work on a task together). When there are just 2 entities and there are no 'twists' to the question, we can use the Work Formula to get to the correct answer.

Work = (A)(B)/(A+B) where A and B are the individual times needed to complete the task.

We're told that two people can paint a room in 3 hours and 5 hours, respectively. We're asked how long it takes the two people, working together, to paint BOTH rooms.

(3)(5)/(3+5) = 15/8 hours to paint ONE room

Notice that the question asks how long it takes to paint BOTH rooms....

(2 rooms)(15/8 hours each) = 30/8 = 15/4 hours

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Kathleen can paint a room in 3 hours, and Anthony can paint an identic  [#permalink]

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29 Dec 2015, 02:38
Bunuel wrote:
Kathleen can paint a room in 3 hours, and Anthony can paint an identical room in 5 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?

A. 8/15
B. 4/3
C. 15/8
D. 9/4
E. 15/4

It is always useful to assume the total work units in such questions. This makes the calculations easier.
Always assume the total work units as the LCM of the time taken.

Assume total work units = 15 units.
Kathleen can paint at $$\frac{15}{3}$$ = 5 units/hour
Anthony can paint at $$\frac{15}{5}$$ = 3 units per hour.

Together they will paint 15 units in $$\frac{15}{{3 + 5}}$$ = $$\frac{15}{8}$$ hours.
Hence time required to pain two such rooms = $$\frac{15}{8}$$ * 2 = $$\frac{15}{4}$$ hours

Option E
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Re: Kathleen can paint a room in 3 hours, and Anthony can paint an identic  [#permalink]

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13 Apr 2016, 10:27
I think everyone understands how to do the problem, as the math is pretty basic and the question time is encountered pretty frequently on the GMAT. The real issue here is: How well do you read the problem?

The reason people get caught up on this question is because they skim the question and think they know how to solve the question immediately, which often results in them missing out on the "BOTH ROOM" piece of the question. So, the takeaway here is: Read the question carefully!

Good luck folks!
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Joined: 28 Mar 2016
Posts: 14
Location: United States (UT)
Re: Kathleen can paint a room in 3 hours, and Anthony can paint an identic  [#permalink]

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13 Apr 2016, 22:54
The available answer choices make this a good question to estimate on and answer the question very quickly.

Assuming they start in different rooms, Kat finishes her room in 3 hours and moves over to Help Anthony, at which point he has 2/5ths of a room left to paint (Since he's been painting his room for the last three hours). So even if Anthony were to sit back and watch Kat do the rest of his painting, she'd have it done in less then an an hour (2/3rds of an hour actually). so with Anthony's help we're looking for a answer greater than 3 and less than 4. which makes answer choice E a great choice.
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Re: Kathleen can paint a room in 3 hours, and Anthony can paint an identic  [#permalink]

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17 Oct 2018, 19:44
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Re: Kathleen can paint a room in 3 hours, and Anthony can paint an identic   [#permalink] 17 Oct 2018, 19:44
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