Let’s say I happen to live at the Equator. And let’s say I happen to have a special plane. My plane can fly as fast as I want; for as long as I want. Let’s also say it’s exactly 12:00 PM (noon) when I take off going directly west.
I continue to fly along the equator all day and it feels like I am tracking the Sun across the face of the earth, i.e. the Sun remains in the same place in the sky relative to my plane (directly overhead). If at some point I decide to land, it will still be 12 noon where ever I happen to set down.
In order to always keep the relative time at 12 noon how fast must I fly? What if instead of flying along the equator I was at 40 degrees latitude? How fast would I have to fly then? And how do I figure it out?
The earth is approximately 24000 statute miles in circumferance. It turns once in 24 hours so your speed at the equator would have to be about 1000 mph. The speed at any latitude angle, l, would be 1000cos(l). In the example you gave it would be 1000cos(40[sup]o[/sup]) = 766 mph.