A mathematician is surfing in Long Beach, New York. He is standing on the shore and wants to paddle out to a spot 40 ft from shore; the closest point on the shore to that spot is 40 ft from where he is now standing. (See the figure.) If he can walk 5 ft per second along the shore and paddle 3 ft per second once he’s in the water, how far along the shore should he walk before paddling toward the desired destination if he wants to complete the trip in the shortest possible time? What is the shortest possible time?

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40 ft 40 ft