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# Help is much appreciated

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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?

Oct 24, 2022

#1
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How many extra day(s) will the remaining bricklayers need?

Hello Guest!

$$C-castle\ building, b-bricklayer, d-days\\ C=\frac{C}{60_b\cdot 16_d}\cdot (5_d\cdot 60_b+(16-5+x)_d\cdot (60-5)_b)\ |\ :C\\ 60\cdot 16=5\cdot 60+(16-5+ x)\cdot 55\\ 960=300+(11+ x)\cdot 55\\ 960=300+605+55x\\ x=\dfrac{960-300-605}{55}\\ \color{blue}x=1$$

The remaining masons need an additional day.

!

Oct 24, 2022
edited by asinus  Oct 24, 2022
edited by asinus  Oct 24, 2022
#2
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I feel dumb

Guest Oct 24, 2022
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asinus  Oct 24, 2022
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Method 1

16 - 5 =11 days' work remains by the original 60 bricklayers

[60  x  16] / 55 =17.4545.....days that would have taken 55 bricklayers to finish the entire work.

But 5/16 of the work is already done and 11 /16 remains.

So: 17.4545...  x  11/16 =12 days for the remaining 55 bricklayers to finish the work

12  +  5  days =17 days, or 1 extra day for the 55 bricklayers to finish the work.

Method 2

Since 60 / 16 =3.75 old rate  and 55 / 11 =5 new rate

Therefore: 3.75 / 5  x  16 days =12 days, or 1 extra day for 55 bricklayers to finish the work.

12  +  5 ==17 days, or 1 extra day.

Method 3

55 / 60 = 0.9166667 of the original 60 bricklayers remain on the job. Therefore the number of days to finish the work will go up to: [1 / 0.9166667]  x 11 days = 12 days.

Oct 24, 2022