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# Wendy can build a birdhouse in 15 hours and Miguel can build

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Wendy can build a birdhouse in 15 hours and Miguel can build [#permalink]  18 Jun 2018, 14:46
Expert's post
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Question Stats:

80% (00:39) correct 20% (00:25) wrong based on 10 sessions
Wendy can build a birdhouse in 15 hours and Miguel can build an identical birdhouse in 10 hours. How many hours will it take Wendy and Miguel, working together at their respective constant rates, to build a birdhouse? (Assume that they can work on the same birdhouse without changing each other’s work rate.)

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
[Reveal] Spoiler: OA

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Joined: 20 Apr 2016
Posts: 826
WE: Engineering (Energy and Utilities)
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Kudos [?]: 603 [0], given: 124

Re: Wendy can build a birdhouse in 15 hours and Miguel can build [#permalink]  02 Jul 2018, 05:07
sandy wrote:
Wendy can build a birdhouse in 15 hours and Miguel can build an identical birdhouse in 10 hours. How many hours will it take Wendy and Miguel, working together at their respective constant rates, to build a birdhouse? (Assume that they can work on the same birdhouse without changing each other’s work rate.)

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

A and B working together can complete a work in = $$\frac{(A*b)}{(A+B)}$$

Wendy and Miguel working together can finish the work in = $$\frac{(15*10)}{(15+10)}$$ $$=\frac{150}{25} = 6 hrs$$
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1782 [0], given: 397

Re: Wendy can build a birdhouse in 15 hours and Miguel can build [#permalink]  07 Jul 2018, 04:43
Expert's post
Explanation

Use two separate lines in a W = RT chart, one for Wendy and one for Miguel, to calculate their respective rates. Building 1 birdhouse equals doing 1 unit of work:

Attachment:

image1.jpg [ 27.92 KiB | Viewed 452 times ]

Thus, Wendy’s rate is $$\frac{1}{15}$$ birdhouses per hour, and Miguel’s rate is $$\frac{1}{10}$$birdhouses per hour. Since Wendy and Miguel are working together, add their rates:

Attachment:

image2.jpg [ 23.85 KiB | Viewed 452 times ]

Now solve for t by first combining the fractions:

$$1=(\frac{1}{15}+\frac{1}{10})t$$

$$1=(\frac{5}{30})t$$

$$t=6$$
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Re: Wendy can build a birdhouse in 15 hours and Miguel can build   [#permalink] 07 Jul 2018, 04:43
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