# 20 workers completed 1/4 of a building in 8 days. Due to a dedication ceremony, it became necessary to complete the building in the next 5 days. How many workers were added to the original 20 to make this possible?

## Assume all workers work at the same rate. The answer is 76, but I'm not sure how to get there.

Feb 28, 2018

#### Explanation:

The amount of construction for 1 day by 20 workers is:
$\frac{1}{4} \div 8 \textcolor{w h i t e}{\text{ddd") ->color(white)("ddd}} \frac{1}{4} \times \frac{1}{8} = \frac{1}{32}$

The amount of construction in 1 day by 1 worker is

$\frac{1}{32} \div 20 \textcolor{w h i t e}{\text{d")->color(white)("d}} \frac{1}{32} \times \frac{1}{20} = \frac{1}{640}$

The above was for $\frac{1}{4}$ of the total build so there is $\frac{3}{4}$ left to build in 5 days.

Let the unknown count of workers be $x$. Then for 5 more days we have:

$\text{day count" xx" daly work rate"xx"worker count"=3/4" buld}$

$\textcolor{w h i t e}{\text{dd")5color(white)("ddddd") xxcolor(white)("dddddd")1/640color(white)("ddd")xxcolor(white)("dddd")xcolor(white)("ddddd}} = \frac{3}{4}$

$5 x = 640 \times \frac{3}{4}$

$5 x = 480$

$x = 96$ Total count

Additional workers is $96 - 20 = 76$