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Three factory employees work at constant rates to produce
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09 Dec 2017, 19:29
09 Dec 2017, 19:29
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Question Stats:
14% (02:57) correct
85% (02:51) wrong based on 35 sessions
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Three factory employees work at constant rates to produce DVDs. Employee A produces y DVDs in \(\frac{2}{5}\) of an hour. Employee B produces y DVDs in \(\frac{3}{5}\) of an hour. Employee C produces y DVDs in \(\frac{5}{4}\) of an hour. Which of the following combinations of employees can produce at least 5y DVDs in 2 hours?
Indicate all such statements.
A. Employee A alone
B. Employee B alone
C. Employee C alone
D. Employees A and B together
E. Employees B and C together
F. Employees A, B, and C together
G. Even if all three employees work together, they will not finish the job
Indicate all such statements.
A. Employee A alone
B. Employee B alone
C. Employee C alone
D. Employees A and B together
E. Employees B and C together
F. Employees A, B, and C together
G. Even if all three employees work together, they will not finish the job
Show: :: OA
A, D, F
Drill 4
Question: 8
Page: 532
Question: 8
Page: 532
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Re: Three factory employees work at constant rates to produce
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23 May 2021, 12:28
23 May 2021, 12:28
2
sandy wrote:
Three factory employees work at constant rates to produce DVDs. Employee A produces y DVDs in \(\frac{2}{5}\) of an hour. Employee B produces y DVDs in \(\frac{3}{5}\) of an hour. Employee C produces y DVDs in \(\frac{5}{4}\) of an hour. Which of the following combinations of employees can produce at least 5y DVDs in 2 hours?
Indicate all such statements.
A. Employee A alone
B. Employee B alone
C. Employee C alone
D. Employees A and B together
E. Employees B and C together
F. Employees A, B, and C together
G. Even if all three employees work together, they will not finish the job
Indicate all such statements.
A. Employee A alone
B. Employee B alone
C. Employee C alone
D. Employees A and B together
E. Employees B and C together
F. Employees A, B, and C together
G. Even if all three employees work together, they will not finish the job
Show: :: OA
A, D, F
Drill 4
Question: 8
Page: 532
Question: 8
Page: 532
Output summary for each employee
Employee A produces y DVDs in 24 minutes
Employee B produces y DVDs in 36 minutes
Employee C produces y DVDs in 75 minutes
We want to determine which combination of employees can produce at least 5y DVDs in 120 minutes
A. Employee A alone
120/24 = 5
So there are 5 24-minute periods in 120 minutes
Since employee A produces y DVDs during every 24-minute period, we know that employee A can produce 5y DVDs in 120 minutes.
Answer choice A works.
Important: Employee A produces EXACTLY 5y DVDs in 120 minutes.
Since employee A is the fastest worker, we know that employees B and C will not be able to produce 5y DVDs in 120 minutes.
Eliminate answer choices B and C.
Also, since employee A can produce 5y DVDs in 120 minutes by himself/herself, any combination of workers that includes employee A will be able to produce at least 5y DVDs in 120 minutes
So, answer choices D and F work.
E. Employees B and C together
120/36 = 3 1/3
So there are 3 1/3 36-minute periods in 120 minutes
Since employee B produces y DVDs during every 36-minute period, we know that employee B can produce (3 1/3)y DVDs in 120 minutes.
120/75 = 1.6
So there are 1.6 75-minute periods in 120 minutes
Since employee C produces y DVDs during every 75-minute period, we know that employee C can produce 1.6y DVDs in 120 minutes.
So if employees B and C work together, the total number of DVDs they can produce = (3 1/3)y + 1.6y, Which is less than 5y.
Eliminate answer choice D.
G. Even if all three employees work together, they will not finish the job
We already concluded that employee A can produce 5y DVDs in 120 minutes by himself/herself
Eliminate answer choice G.
Answer: A, D and F
General Discussion
Re: Three factory employees work at constant rates to produce
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29 Dec 2017, 16:43
29 Dec 2017, 16:43
Expert Reply
Explanation
Plug in for y. If y = 30, then Employee A produces 30 DVDs in \(\frac{2}{5}\) of an hour, so using a Rate Pie you can figure out that his rate is 75 DVDs per hour. Employee B produces 30 DVDs in of \(\frac{3}{5}\) an hour, so his rate is 50 DVDs per hour. Employee C produces 30 DVDs \(\frac{5}{4}\) in of an hour, so his rate is 24 DVDs per hour.
5y = 150, so you need to find the combination of employees that can produce 150 DVDs in 2 hours. Employee A will produce exactly 150 DVDs in 2 hours, so choice (A) is a credited answer. If you know that Employee A alone can produce 5y DVDs in 2 hours, then choices (D) and (F) must also be correct answers, and choice (G) must be incorrect.
Employee B will only produce 100 DVDs in 2 hours, so you can eliminate choice (B). Employee C will only produce 48 DVDs in 2 hours, so you can also eliminate choice (C). If Employees B and C work together for 2 hours, they will produce 148 DVDs, so choice (E) is incorrect.
Plug in for y. If y = 30, then Employee A produces 30 DVDs in \(\frac{2}{5}\) of an hour, so using a Rate Pie you can figure out that his rate is 75 DVDs per hour. Employee B produces 30 DVDs in of \(\frac{3}{5}\) an hour, so his rate is 50 DVDs per hour. Employee C produces 30 DVDs \(\frac{5}{4}\) in of an hour, so his rate is 24 DVDs per hour.
5y = 150, so you need to find the combination of employees that can produce 150 DVDs in 2 hours. Employee A will produce exactly 150 DVDs in 2 hours, so choice (A) is a credited answer. If you know that Employee A alone can produce 5y DVDs in 2 hours, then choices (D) and (F) must also be correct answers, and choice (G) must be incorrect.
Employee B will only produce 100 DVDs in 2 hours, so you can eliminate choice (B). Employee C will only produce 48 DVDs in 2 hours, so you can also eliminate choice (C). If Employees B and C work together for 2 hours, they will produce 148 DVDs, so choice (E) is incorrect.
