Very simple optimization problem

truck_time.py

# The wreck of a plane in a desert is 15 miles from the nearest point A on a straight road.
# A rescue truck starts for the wreck at a point on the road that is 30 miles distant from A.
# If the truck can travel at 80 mph on the road and at 40 mph on a straight path in the desert,
# how far from A should the truck leave the road to reach the wreck in a minimum time?

from math import sqrt

def truck_time(turn_point):
    road_distance = turn_point
    skipped_road_distance = 30 - turn_point
    desert_distance = sqrt(skipped_road_distance ** 2 + 15 ** 2)
    
    road_time = road_distance / 80.0
    desert_time = desert_distance / 40
    return road_time + desert_time

for i in xrange(0, 30):
    print "Turning at %s results in %s h" % (i, truck_time(i))

# Minimum is around 22, which agrees with intuitive guess 30 * (1/sqrt(2))

cool :D