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

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Retired Moderator
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Joined: 07 Jun 2014
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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] New post 18 Jun 2018, 14:46
Expert's post
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Question Stats:

92% (00:44) correct 7% (00:17) wrong based on 38 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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VP
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Re: Wendy can build a birdhouse in 15 hours and Miguel can build [#permalink] New post 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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Retired Moderator
User avatar
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2911 [0], given: 394

Re: Wendy can build a birdhouse in 15 hours and Miguel can build [#permalink] New post 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
image1.jpg [ 27.92 KiB | Viewed 1678 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
image2.jpg [ 23.85 KiB | Viewed 1681 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] New post 09 Jul 2019, 05:50
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



this is an easy type of question.
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Re: Wendy can build a birdhouse in 15 hours and Miguel can build   [#permalink] 09 Jul 2019, 05:50
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