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?
+14905 How many extra day(s) will the remaining bricklayers need?
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\(C-castle\ building, b-bricklayer, d-days\\ C=\frac{C}{60_b\cdot 16_d}\cdot (5_d\cdot 60_b+(16-5+x)_d\cdot (60-5)_b)\ |\ :C\\ 60\cdot 16=5\cdot 60+(16-5+ x)\cdot 55\\ 960=300+(11+ x)\cdot 55\\ 960=300+605+55x\\ x=\dfrac{960-300-605}{55}\\ \color{blue}x=1\)
The remaining masons need an additional day.
!
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.
