At 8am on Thursday, two workers, A and B, each start working independe

I started by taking ranges for B. A completed the work in 16hours while B completed the work by a minimum of 8 hours and a maximum of 12 hours. Working out with 2 values for B, I will be able to get the range of the time required for A and B to complete the work together which comes out to be 48/9 and 48/7 hours i.e 5.4 hours (Thursday 1:24 PM) and 6.85 hours ( Thursday 2:51 PM) . I am able to narrow down to A and B ... Since A is falling too much on one side of the beam i think i would go with B .. Please comment on my approach

To finish the work independently,

A - 16 hours
8 hours < B < 12hours

To finish the work together they will take,

16/3 hours < A +B < 48/7 hours

approximately, A and B working together take between 5.3hours and 6.8 hours to finish the work together.

Therefore ans is (C)

MANHATTAN GMAT OFFICIAL SOLUTION:

This is a combined work problem. The required work is one lamp and the question asks for the time taken, so you need to determine something about the rates of the workers.

Worker A’s rate can be calculated. She works for 2 full days, or 16 hours, to complete one lamp. Therefore, she completes 1/16 lamp per hour.

However, Worker B’s rate is trickier to determine. She takes one full day and some part of the next morning. The first day is 8 hours and the morning shift is 4 hours, so she works on the lamp for more than 8 hours and less than 12 hours. Therefore, her rate is greater than 1/12 lot per hour but less than 1/8 lot per hour.

Add this information to an RTW chart.
Remember that RT = W!

Because the work quantity is 1 lamp, express the time, t, as 1/Rate (that is, the reciprocal of the rate). The range of possible values for the time is 16/3 < t < 48/7. This translates to the following:

5 and 1/3 hours < t < 6 and 6/7 hours
1/3 of an hour is 20 minutes, so the lower boundary is 5 hours 20 minutes. 6/7 of an hour is a bit more annoying to calculate; check the answers first to see whether this is really necessary.

The workers start at 8am on Thursday and take a 1-hour break between 12 and 1pm, so if they worked together, they would complete the job after 2:20pm but a little before 4:00pm on Thursday. Only one answer choice fits: 3pm.

Alternatively, you could use estimation, though recognize that you might not always be able to narrow all the way down to one answer choice. In many cases, though, you can (including this case!). It’s surprising how often you can get to the right answer this way on rate questions.

When working together, the two workers must use at least the entire 4-hour shift on Thursday morning because the first answer choice is Thursday afternoon.

Worker A takes 16 hours to complete one lamp. Therefore, she completes 1/4 of a lamp during a 4-hour shift.

Worker B takes between 8 and 12 hours to complete one lamp. Therefore, she completes between 1/3 and 1/2 of a lamp during a 4-hour shift.

At the end of the Thursday morning shift, then, the workers have finished somewhere between (1/4 + 1/3) and (1/4 + 1/2) of a lamp, or between 7/12 and 3/4 of a lamp. They’ve completed more than half of the lamp during the first 4-hour shift, so they won’t need another complete 4-hour shift to finish; eliminate answer (E).

If they’ve completed 3/4 of the lamp, then they only have 1/4 to go. 1/4 of a lamp represents one-third of the work they did during the first 4 hours, so they’ll need another 4(1/3) hours to finish, or 1 hour 20 minutes. Therefore, they need at least until 2:20pm on Thursday afternoon. Eliminate answers (A) and (B).

One end of the possible time range is 2:20pm; the other end must include one of the two remaining answers but exclude the other one. Answer (C) must be it. If you want to prove it to yourself, finish off the estimation (but note that logic tells you that you can’t include D in the final range without including C!).

If the workers finish 7/12 of the lamp in 4 hours, then they need a bit less than the 4 hours of the second shift to finish off the other 5/12 of the lamp. Specifically, they need 5/7 of that second shift. That’s an annoying number. 5/8 is 62.5%. 5/6 is about 83%. So let’s call 5/7 about 70% (note that this is a bit of an underestimate).

75% of 4 hours is 3 hours, so the workers need a bit less than 3 hours after lunch to finish off the lamp. They’ll be done by 4p; eliminate answer (D).

The correct answer is (C).

thanks for a great question... and even clearer and better explanations to one and all.....Buel every post of yours deserves a kudo... thanks for the question

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.

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 ⅓ 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

Great question.

Absolutely loved Lucky2783's approach.

I solved using the same but sort of half baked. Just bumping it up

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