The set-up is easier than you think . . . A hunter is at a point on a straight river bank running east-west.
He wants to get to his cabin located 3 miles north and 8 miles west.
He can travel 5 mph on the river but only 2 mph on the rocky land.
How far upriver should he go in order to reach the cabin in minimum time?
: - - - - 8 - - - - :
C 8-x P x A
o - - - - - o - - - - o
_____ * | 3
√x²+3² * |
The hunter is at
He wants to get to his cabin
He crosses the river to point
then hikes the remaining distance to
The distance across the river is: , miles.
. . At 5 mph, this will take him: . hours.
The distance he hikes on rocky land is: . miles.
. . At 2 mph, this will take him: . hours.
Hence, his total time is: . hours.
And that is the function we must minimize.