A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C diametrically opposite A on the other side of the lake. She can bicycle at the rate of 6 mi/h and row a boat at 3 mi/h. What is the shortest amount of time she can travel to point C?

Answer 1

Take a look here:

math.stackexchange.com/questions/839014/optimization-problem-not-sure-how-to-proceed

Answer 2

Boat: V * t = 4 mi.
t = 4/V = 4/3 = 1.33 h.

Bicycle: The distance is 1/2 circle.
d = pi * 2r/2 = pi * r = 3.14 * 2 = 6.28 mi.
V * t = 6.28.
t = 6.28/V = 6.28/6 = 1.05 h. = Shortest time.