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Stockmoose16
- Master | Next Rank: 500 Posts
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Can someone explain the math for the following problem?
Two machines are sawing wood but due to space limitations only one at a time can operate. Machine A is used for the first shift and the other machine for the second shift, while both work half of the third shift. Machine A can do the job in 12 days if it worked two shifts and Machine B can do the job in 15 days if it worked two shifts. How many days will it take to do the job with current work schedule?
A.14
B.13
C.11
D.9
E.7
The following was posted in another thread but I don't understand how he converts 2 shifts a day to 1.5 shifts a day by multiplying 2/1.5.
In my mind, if it takes 12 days to complete doing 2 shifts per day, then it should take 25% longer (since you're losing 25% of the shifts) to do it in 1.5 shifts. Thus, shouldn't it take 15 days (not 16 days) for machine A to complete the job?
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Total 3 shifts worked per day, with each machine working for 1.5 shifts
Machine A:
2 shifts a day...................12 days to complete the work
1.5 shifts/day...................12*2/1.5 = 16 days to complete the work
in one day it does 1/16 of work
Machine B:
2 shifts a day...................15 days to complete the work
1.5 shifts/day...................15*2/1.5 = 20 days to complete the work
in one day it does 1/20 of work
working together they do 1/16 + 1/20 = 9/80 of work in a day
they complete the work in 80/9 = 9 approx
IMO: D
Two machines are sawing wood but due to space limitations only one at a time can operate. Machine A is used for the first shift and the other machine for the second shift, while both work half of the third shift. Machine A can do the job in 12 days if it worked two shifts and Machine B can do the job in 15 days if it worked two shifts. How many days will it take to do the job with current work schedule?
A.14
B.13
C.11
D.9
E.7
The following was posted in another thread but I don't understand how he converts 2 shifts a day to 1.5 shifts a day by multiplying 2/1.5.
In my mind, if it takes 12 days to complete doing 2 shifts per day, then it should take 25% longer (since you're losing 25% of the shifts) to do it in 1.5 shifts. Thus, shouldn't it take 15 days (not 16 days) for machine A to complete the job?
-----------------
Total 3 shifts worked per day, with each machine working for 1.5 shifts
Machine A:
2 shifts a day...................12 days to complete the work
1.5 shifts/day...................12*2/1.5 = 16 days to complete the work
in one day it does 1/16 of work
Machine B:
2 shifts a day...................15 days to complete the work
1.5 shifts/day...................15*2/1.5 = 20 days to complete the work
in one day it does 1/20 of work
working together they do 1/16 + 1/20 = 9/80 of work in a day
they complete the work in 80/9 = 9 approx
IMO: D
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