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60 bricklayers began a 16-day project to build a castle. After five days, five of the bricklayers quit the job. If they work the same amount each day, how many extra day(s) (beyond the original estimate of 16) will the remaining bricklayers need?

 Nov 20, 2022
 #1
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You can use proportional relationships:

 

60 brick-layers -> 16-day project

 

15/4 brick-layers -> 1-day project

 

15/4*5 brick-layers -> 5-day project

 

So the bricklayers will need an extra 5 days.

 Nov 20, 2022
 #2
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16  -  5 ==11 days' work remains

 

11 / 16 - ratio of the work that remains

 

[60  x  16] / 55 ==17.4545.... what would have taken 55 men to finish the original work.

 

But only 11 / 16 of the original work remains, therefore:

 

So:17.454545.....  x  11/16 ==12 days that would take 55 men to finish, or 1 extra day.

 

In total: 5 + 12 ==17 days to finish the work, or 1 extra day due to departure of 5 men.

 Nov 20, 2022
 #3
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+1

There is a decrease in manpower of:

 

1  -  [55 / 60] = 1/12

 

Therefore it takes 12 days, instead of 11,  for the remaining 55 men to finish the work. 

 

So, instead of the original 16 days, it will take:

 

5  +  12 == 17 days to finish the work.

 Nov 20, 2022

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