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Two dressmakers, Sue and Anne, sewed costumes for a local theater production. Sue sewing alone for 10 hours sewed some

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by BTGmoderatorDC » Wed Jan 06, 2021 4:48 pm

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Two dressmakers, Sue and Anne, sewed costumes for a local theater production. Sue sewing alone for 10 hours sewed some of the costumes, Anne sewing for 16 hours finished sewing the remaining costumes. How any hours would it have taken Sue alone to sew all of the costumes?

(1) Sue sewed 1 costume every 2 hours.
(2) Sue sewed twice as many costumes working in 10 hours as Anne produced in 16 hours.



OA B

Source: Princeton Review
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Re: Two dressmakers, Sue and Anne, sewed costumes for a local theater production. Sue sewing alone for 10 hours sewed so

by swerve » Thu Jan 07, 2021 10:18 am
BTGmoderatorDC wrote: ↑
Wed Jan 06, 2021 4:48 pm
 Two dressmakers, Sue and Anne, sewed costumes for a local theater production. Sue sewing alone for 10 hours sewed some of the costumes, Anne sewing for 16 hours finished sewing the remaining costumes. How any hours would it have taken Sue alone to sew all of the costumes?

(1) Sue sewed 1 costume every 2 hours.
(2) Sue sewed twice as many costumes working in 10 hours as Anne produced in 16 hours.



OA B

Source: Princeton Review
Amount of work done by Sue per hour \(= s\)
Amount of work done by Anne per hour \(= a\)
Total work done \(= w\)
\(10s + 16a = w\)

1. Sue sewed costume per hour \(s=\frac{1}{2}\) costume per hour. Not sufficient \(\Large{\color{red}\chi}\)

2. \(10s = 2\cdot(16a) \Rightarrow 5s = 16a\)

Sue will need \(5\) hours to complete Anne's part of the job.
Sue will complete the entire work in \(10+5=15\) hours working alone. Sufficient \(\Large{\color{green}\checkmark}\)

Therefore, B
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