Non veni pacem mittere, sed gladium.
I think that the gator goes wherever he wants to and eats what he wants to.
With a quick Google search, it looks like larger gators top out around 8-10 mph, smaller ones can reach 25 mph. Texas Fish and Game says they can reach 35 mph.
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It's all fun and games unless he sees you first.
Gators are ambush predators. You should never walk your dog near the water's edge in South Florida.