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.

1 Answer
Tony B
Feb 28, 2018

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=1/3214÷8ddd→ddd14×18=132

The amount of construction in 1 day by 1 worker is

1/32-:20color(white)("d")->color(white)("d")1/32xx1/20=1/640132÷20d→d132×120=1640

The above was for 1/414 of the total build so there is 3/434 left to build in 5 days.

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

"day count" xx" daly work rate"xx"worker count"=3/4" buld" day count× daly work rate×worker count=34 buld

color(white)("dd")5color(white)("ddddd") xxcolor(white)("dddddd")1/640color(white)("ddd")xxcolor(white)("dddd")xcolor(white)("ddddd")=3/4dd5ddddd×dddddd1640ddd×ddddxddddd=34

5x=640xx3/45x=640×34

5x=4805x=480

x=96x=96 Total count

Additional workers is 96-20=7696−20=76

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