I was reading this analogy of Fermat's Principle of Least Time:
In Figure, our problem is to go from A to B in the shortest time. To illustrate that the best thing to do is not just to go in a straight line, let us imagine that a beautiful girl has fallen out of a boat, and she is screaming for help in the water at point B. The line marked x is the shoreline. We are at point A on land, and we see the accident, and we can run and can also swim. But we can run faster than we can swim. What do we do? Do we go in a straight line? (Yes, no doubt!) However, by using a little more intelligence we would realize that it would be advantageous to travel a little greater distance on land to decrease the distance in the water because we go so much slower in the water.
I am thinking that our speed on land is faster than in water so to reach in the least time, we must minimize our distance in the water. So we would take the path $AMB$ ($MB\perp x$).
Why would we take path $ACB$?
Is it because $AM$ is increased by a large factor?