Its funny that this hasn’t been mentioned, yet I’ve experienced this a couple of times. I’ve been in flights where the pilot has requested a change in altitude so they can catch a better tailwind. I was on a corporate Learjet rigged out as an ambulance (I mention this as the option may not be available on commercial airliners) and they requested an increase in altitude. It was a while ago, but we crossed from California to Toronto in a lot less time. He mentioned the relative ground speed and it was insane.
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