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

Decoding everything, worker B makes a lamp in 16 hours, and worker A makes a lamp in somewhere between 8 and 12 hours. We'll find the minimum time it might take them together if we assume A takes exactly 8 hours. In that case, using any rates method you like (e.g. if A makes one lamp in 8 hours, A makes 2 lamps in 16 hours, so together A+B will make 3 lamps in 16 hours, or one lamp every 16/3 hours = 5h20m), we find it takes them at least 5h20m. So accounting for their one hour lunch break, they must finish the lamp after 2:20pm on Thursday, working together. Now we could also find the maximum time they could need together, but that's unnecessary. There can only be one right answer to a GMAT question, so whatever maximum we find, it will need to make one answer choice possible and the rest impossible. So whatever that maximum is, it will need to make 3:00pm Thursday possible, but any later choice impossible, and only C can be correct.

BTGmoderatorDC wrote:At 8am on Thursday, two workers, A and B, each start working independently to build identical decorative lamps. Worker A completes her lamp at 5pm on Friday, while Worker B completes her lamp sometime during the morning on Friday. If both workers adhere to working hours of 8am to 12pm and 1pm to 5pm 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, 1:30pm
B. Thursday, 2:15pm
C. Thursday, 3:00pm
D. Thursday, 4:15pm
E. Friday, 12:00pm

OA C

Source: Manhattan Prep

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 workdays (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, respectively, of worker B’s rate..

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 be 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