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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