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Wendy can build a birdhouse in 15 hours and Miguel can build
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18 Jun 2018, 14:46
18 Jun 2018, 14:46
Expert Reply
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Question Stats:
94% (00:54) correct
5% (00:37) wrong based on 84 sessions
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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) 5
(B) 6
(C) 7
(D) 8
(E) 9
Re: Wendy can build a birdhouse in 15 hours and Miguel can build
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02 Jul 2018, 05:07
02 Jul 2018, 05:07
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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) 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 = \(\frac{(15*10)}{(15+10)}\) \(=\frac{150}{25} = 6 hrs\)
Re: Wendy can build a birdhouse in 15 hours and Miguel can build
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07 Jul 2018, 04:43
07 Jul 2018, 04:43
1
Expert Reply
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:
image1.jpg [ 27.92 KiB | Viewed 5712 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:
image2.jpg [ 23.85 KiB | Viewed 5711 times ]
Now solve for t by first combining the fractions:
\(1=(\frac{1}{15}+\frac{1}{10})t\)
\(1=(\frac{5}{30})t\)
\(t=6\)
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 5712 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 5711 times ]
Now solve for t by first combining the fractions:
\(1=(\frac{1}{15}+\frac{1}{10})t\)
\(1=(\frac{5}{30})t\)
\(t=6\)
