Yep, at 67, I experience the exact same thing, burn in the quads, etc.. In fact, I try to ride in to what I think are going to be spirited rides so I can get warmed up in advance. Same as you, a short rest after 8 miles or so and I'm good to go. The rest of the ride, the legs feel great.
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“Train hard until your legs are tanned, then keep going until the shape arrives.” -Jolanda Neff