Question

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.

Answer 1

I get 76 additional workers.

Explanation:

The amount of construction for 1 day by 20 workers is:
`1/4-:8 color(white)("ddd") ->color(white)("ddd")1/4xx1/8=1/32`

The amount of construction in 1 day by 1 worker is

`1/32-:20color(white)("d")->color(white)("d")1/32xx1/20=1/640`

The above was for `1/4` of the total build so there is `3/4` left to build in 5 days.

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

`"day count" xx" daly work rate"xx"worker count"=3/4" buld"`

`color(white)("dd")5color(white)("ddddd") xxcolor(white)("dddddd")1/640color(white)("ddd")xxcolor(white)("dddd")xcolor(white)("ddddd")=3/4`

`5x=640xx3/4`

`5x=480`

`x=96` Total count

Additional workers is `96-20=76`