College Algebra & Trigonometry, 2018a

252 CHAPTER 4. FUNCTIONS
Distance/Time (or Cost) Optimization
At Noon, a dune buggy is in the desert at the point A indicated below. Point A is
40km from a paved road, which covers the 50 km between points B and D.
If the dune buggy can travel 45 kph in the desert and 75 kph on the road, where
is the best place for the driver to leave the desert and turn onto the road in order
to minimize the travel time?
What time does the driver arrive at Point D assuming they follow the path for
minimal travel time?
B
50 km
D
40 km
A
One option is that the dune buggy can travel in a straight line from A to B (at 45
kph) and then travel on the paved road from B to D (at 75 kph). This would take
1.5 hrs.
Another option is for the dune buggy to travel straight from A to D at 45 kph.
The distance here is about 64 km (found using the Pythagorean Theorem). That
means the travel time would be about 1.423 hrs.
The optimization here says that, if the dune buggy were to travel part of the way
in the desert (along a diagonal) and the rest of the way on the paved road, then
there might be a minimal time that is shorter than the 1.423 hrs. it would take
going straight from A to D.