First, unless you're flying a business jet for someone who doesn't care about fuel I doubt you're flying at Mach .82 as a standard cruising speed. You don't have to shave 30 minutes off a 7 hour journey. Sometimes 15 minutes is all it takes to make a connection

Headwind and tailwind don't play into airspeed. They have an effect on groundspeed. Winds don't have an effect on the aircraft's max airspeed, all that matters is the relative velocity of the air going past the aircraft.

An aircraft flying at 500 mph airspeed with a tailwind on 100 mph is flying at a groundspeed of 600 mph, conversely a 100 mph headwind translates into a groundspeed of 400 mph.