Question

If it takes 3 workers 8 days to paint a fence how long would it take 4 workers​

Answer 1

so 3 guys can do the whole work in 8 days, that means that for one day the same 3 guys are doing (1/8)th of the whole work, let's divide that 1/8 by 3 to see how much each guy does rate wise

`\stackrel{ \begin{array}{llll} \textit{fraction of}\\ \textit{the whole done}\\ \textit{by all 3} \end{array} }{\cfrac{1}{8}} / \stackrel{ workers }{3}\implies \cfrac{1}{8}\cdot \cfrac{1}{3}\implies \cfrac{1}{24}\impliedby \begin{array}{llll} \textit{fraction done}\\ \textit{by just 1 worker} \end{array}`

now, we know is 1/8 th because the whole thing took 8 days, so for 1 day is just 1/8 of 8, and now we know each worker is really doing 1/24 th per day of the whole thing.

now, let's add another worker, who is going to be going at the same speed as the other 3 guys, or 1/24 of the work, so the work will take "t" days total, so in 1 day all those 4 guys will be doing only (1/t)th of the whole thing, so

`\stackrel{ \textit{rate for 4 workers} }{\cfrac{1}{24}+\cfrac{1}{24}+\cfrac{1}{24}+\cfrac{1}{24}}~~ = ~~\stackrel{ \textit{fraction of total} }{\cfrac{1}{t}} \\\\\\ \cfrac{4}{24}=\cfrac{1}{t}\implies \cfrac{1}{6}=\cfrac{1}{t}\implies t=6 ~~ days`