First, let's convert the mixed number 1 1/2 to the improper fraction 3/2. We're given that it takes 3/2 days to install 3/5 of a fence. We're looking for how long it takes to install one whole fence - or 5/5 of a fence. To determine that, let's first find out how long it takes to install 1/5 of a fence, and then multiply that quantity by 5 to obtain our answer.
If it takes 3/2 days (3 half-days) to install 3/5 of a fence (3 fifths of a fence), then it makes sense that it would take 1/2 day (1 half-day) to install 1/5 of a fence (1 fifth of a fence).
If it takes 1/2 day to install 1/5 of a fence, then it should take 5 times that amount of time to install all 5/5 of it, or 5 * (1/2) = 5/2 days, or 2 1/2 days as a mixed number.