so two fellows did all the carpeting in 10 days.
now, how long did "1" fellow work only? well, it worked for 10 days.
how long did the other fellow work for? well, it was working alongside the first one, and it was there for also 10 days.
so the two guys working together, really did 10+10 = 20 "days worth of work". So that the whole carpeting job can be done in 20 "days worth of work".
now if we want to finish it in 4 days, 20 ÷ 4 = 5.
so if we hire 5 guys, since each one will do 4 days worth, 5*4 = 20 <- the whole job.