At 8 am on Thursday, two workers, A and B, each start working independently to build identical decorative lamps. Worker A completes her lamp at 5 pm on Friday, while Worker B completes her lamp sometime during the morning on Friday. If both workers adhere to working hours of 8 am to 12 pm and 1 pm to 5 pm each day, at which of the following times might the two workers have completed a single lamp had they worked together at their respective constant rates?
A. Thursday, 1:30 pm
B. Thursday, 2:15 pm
C. Thursday, 3:00 pm
D. Thursday, 4:15 pm
E. Friday, 12:00 pm
The OA is C.
Please, can anyone explain this PS question for me? I can't get the correct answer. I need help to solve it. Thanks.
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At 8am on Thursday, two workers, A and B, each start working
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Worker A takes two 8-hour days to produce a lamp, for a total of 16 hours.swerve wrote:At 8 am on Thursday, two workers, A and B, each start working independently to build identical decorative lamps. Worker A completes her lamp at 5 pm on Friday, while Worker B completes her lamp sometime during the morning on Friday. If both workers adhere to working hours of 8 am to 12 pm and 1 pm to 5 pm each day, at which of the following times might the two workers have completed a single lamp had they worked together at their respective constant rates?
A. Thursday, 1:30 pm
B. Thursday, 2:15 pm
C. Thursday, 3:00 pm
D. Thursday, 4:15 pm
E. Friday, 12:00 pm
Since Worker B finishes sometime Friday morning, B takes between 8 and 12 hours to produce a lamp.
Let each lamp = 48 units.
A's rate = w/t = 48/16 = 3 unit per hour.
If B takes 8 hours to produce a lamp, B's rate = w/t = 48/8 = 6 units per hour.
If B takes 12 hours to produce a lamp. B's rate = w/t = 48/12 = 4 units per hour.
Thus, B's rate must be BETWEEN 4 units per hour and 6 units per hour, implying that the combined rate for A and B must be between 3+4=7 units per hour and 3+6=9 units per hour.
If A and B work at 7 units per hour, the time produce a 48-unit lamp = 48/7 ≈ 7 hours.
If A and B work at 9 units per hour, the time produce a 48-unit lamp = 48/9 = 5.33 hours.
Since the rate for A and B together must be between 7 units per hour and 9 units per hour, the time for them to produce one 48-unit lamp must be MORE THAN 5.33 HOURS but LESS THAN 7 HOURS.
5.33 hours = (8am to 12pm) + (1pm to 2:15pm).
7 hours = (8am to 12pm) + (1pm to 4pm).
The times in blue imply that the lamp will be completed sometime between 2:15pm and 4pm.
The correct answer is C.
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We see that a workday is 8 hours (4 hours in the morning and 4 hours in the afternoon). Thus, it takes 2 workdays, or 16 hours, for worker A to complete her lamp, and therefore, her rate is 1/16. We are given that worker B completes her lamp sometime during the morning on Friday. Thus, it takes her more than 1 workday (or 8 hours) and less than 1 ½ workday (or 12 hours) to complete her lamp, and therefore, her rate is greater than 1/12 but less than 1/8. These two rates are the lower and upper bounds of worker B's rate, respectively.swerve wrote:At 8 am on Thursday, two workers, A and B, each start working independently to build identical decorative lamps. Worker A completes her lamp at 5 pm on Friday, while Worker B completes her lamp sometime during the morning on Friday. If both workers adhere to working hours of 8 am to 12 pm and 1 pm to 5 pm each day, at which of the following times might the two workers have completed a single lamp had they worked together at their respective constant rates?
A. Thursday, 1:30 pm
B. Thursday, 2:15 pm
C. Thursday, 3:00 pm
D. Thursday, 4:15 pm
E. Friday, 12:00 pm
At the upper bound of worker B's rate, if the two workers work together, it will take 1/(1/16 + 1/8) = 1/(1/16 + 2/16) = 1/(3/16) = 16/3 = 5 1/3 hr = 5 hr 20 min to complete one single lamp. Therefore, they will finish by 2:20 pm on Thursday (4 hours from 8 am to 12 pm and 1 hr 20 min after 1 pm).
At the lower bound of worker B's rate, if the two workers work together, it will take 1/(1/16 + 1/12) = 1/(3/48 + 4/48) = 1/(7/48) = 48/7 = 6 6/7 hr ≈ 6 hr 51 min to complete one single lamp. Therefore, they will finish by 3:51 pm on Thursday (4 hours from 8 am to 12 pm and 2 hr 51 min after 1 pm).
Since worker B's rate is between 1/12 and 1/8, the time when they work together will between 2:20 pm and 3:51 pm on Thursday. The only time in the given answer choices is choice C: Thursday, 3:00 pm. Thus choice C is the correct answer.
Answer: C
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