How long does it take?

Let's say you're in a car, some distance away from your home.  You change your speed so that once you're x miles away, you travel at x mph.  How long will it take to get home, approximately?  Consider two specific cases:

1) You change your speed continiously, so that at, say, 7.5 miles away, you're traveling at 7.5 miles per hour.

2) You drop your speed by one mile an hour for every mile traveled.  That is, at 7 miles away, you go to 7 mph, holding that speed for a mile, then going down to 6 mph at a distance of 6 miles away.

Does it matter how far away you are when you start?

Yes it matters how far you are away. It's a simple linear situation. The time required to go from x=7 to x=0 will always be the same no matter what your starting distance is.