Time, distance, rate optimization problems.

1. The best way to get
from here to there ...
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Optimization Problems
Crossing Paths by flickr user dnudson

2. Problem: Suppose you are in the middle of a desert ( point A )
and you want to get to the town ( point B ) as fast as possible. Of
course you can go straight from A to B, but you cannot move too
fast in the desert. Going to the road first ( point S ) and hitching a
ride there might be a better choice. So here is the problem: How
to choose point S so as to minimize the time T it takes to get
from A to B?

3. A man is in the desert 5 miles east of city A which is 5 miles north of
city B along a road. If the man can drive 15 mph in the desert and
35 mph along the road, then at what location along the road should
the man drive to so that the time to travel from where he is to city B
is a minimum?