Question

In the example problem, why are the 8 minutes being subtracted from 6:15pm since the longitude is 73 degrees West?

It states that West sunsets are experienced "later" (we add time) and East sunsets are "earlier" (we subtract time).

Answer 1

Good question. What they mean to say is that locations that are "more East" are earlier, while locations that are "more West" are later.

The starting city was at a longitude of 75* West. Notice that 73* West is more to the East than the starting city (in other words, it is "less West"), while 78* West is more to the west than the starting city.

This is why we subtract 8 minutes going to 73* West from 75* West.