Jane and Ashley take 20 days and 40 days respectively to

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Tue May 01, 2018 8:32 am

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Jane and Ashley take 20 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight-day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project?

A. 10 Days
B. 15 Days
C. 16 Days
D. 18 Days
E. 20 Days

The OA is E.

Please, can anyone explain this PS question for me? I tried to solve it but I can't get the correct answer. Thanks.

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Source: Beat The GMAT — Problem Solving | Tue May 01, 2018 8:32 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue May 01, 2018 8:58 am

swerve wrote:Jane and Ashley take 20 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight-day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project?

A. 10 Days
B. 15 Days
C. 16 Days
D. 18 Days
E. 20 Days

Let the job = the LCM of 20 and 40 = 40 units.

Since Jane takes 20 days to produce the 40-unit job, Jane's rate = w/r = 40/20 = 2 units per day.
Since Ashley takes 40 days to produce the 40-unit job, Jane's rate = w/r = 40/40 = 1 unit per day.

During Jane's 8-day break, Ashely works alone for 8 days.
Since Ashley's rate = 1 unit per day, the work produced by Ashley over these 8 days = rt = 1*8 = 8 units.

To finish the project, Jane works alone 4 extra days.
Since Jane's rate = 2 units per day, the work produced by Jane over these 4 days = rt = 2*4 = 8 units.

Remaining work = (total job) - (work produced by Ashley alone) - (work produced by Jane alone) = 40 - 8 - 8 = 24 units.
Since Jane's rate = 2 units per day and Ashley's rate = 1 unit per day, the combined rate for Jane and Ashley working together = 2+1 = 3 units per day.
Since their combined rate = 3 units per day, the time for Jane and Ashley together to produce the remaining 24 units = w/r = 24/3 = 8 days.

Total time = (Ashley's time alone) + (Jane's time alone) + (time for Jane and Ashley together) = 8 + 4 + 8 = 20 days.

The correct answer is E.

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Sionainn@PrincetonReview: GMAT Instructor; Posts: 41; Joined: Mon Mar 12, 2018 9:54 amFollowed by: 1 member

by Sionainn@PrincetonReview » Tue May 01, 2018 9:08 am

For rate problems, we want to use the formula amount (or work) = rate * time. In cases like this where they don't define a job and instead gives us a time period to complete a job, it is helpful to plug in an amount for the job. This help avoid working with fractional rates when solving.

Pick a number that works well with the numbers in the problem. So in this case, let's say there are 200 pages in a job Now we can find individual rates for Jane (200/20 = 10 pages/day) and Ashley (200/40 = 5 pages/day). Then days that both are working then have a combined rate of 15 pages/day.

We know there are 8 days that will just be Ashley so the rate will be 5 pages/day on those days and a total of 40 pages (8 days * 5 pages/day) will be completed over that period.

We also know there are 4 days that will just be Jane. So on those days the rate will be 10 pages/day and a total of 40 pages (4 days * 10 pages/day) will be completed over that period.

So far we have accounted for 80 pages with the days they are working by themselves. Then there are 120 pages left to complete the job (200 page job - 80 pages completed). These days both of them are working, so the rate is 15 pages/day, so we can find there are 8 days they work together (120 pages/(15 pages/day)).

Then add up the number of days: 8 days both working + 4 days Jane only + 4 days Ashley only = 16 days or choice E.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Thu May 03, 2018 3:29 pm

swerve wrote:Jane and Ashley take 20 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight-day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project?

A. 10 Days
B. 15 Days
C. 16 Days
D. 18 Days
E. 20 Days

Jane's rate is 1/20, Ashley's rate is 1/40, and their combined rate is 1/20 + 1/40 = 2/40 + 1/40 = 3/40. We can let n = the number of days they actually worked together and create the equation:

Together + Ashley alone + Jane alone = 1 job

(3/40)n + (1/40)8 + (1/20)4 = 1

3n/40 + 8/40 + 4/20 = 1

Multiplying by 40 we have:

3n + 8 + 8 = 40

3n = 24

n = 8

So it took 8 + 8 + 4 = 20 days to complete the project.

Answer: E

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