@rohtarantula,
I suspect I'm missing something, but here goes nothing ...
The earth has an equatorial diameter of 12,756.2 km, and we add 20 km to that to get the net diameter of the plane's "orbit," which is 12,776.2 km. Multiply by pi to get ~40137.6 km of circumference. Now, there are no special tricks involved; the sun moves through the sky at around 15 degrees of arc (or 15x the diameter of its disc) per hour. Therefore, it illuminates the surface of the earth at the equator at 15 degrees of longitude per hour. 360/15 = 24, so we divide the circumference of the "orbit" by 24 to get a speed of
1,672 kph, or about mach 1.4.
Of course, as I said, this riddle seems deceptively simple, so I will not be surprised at all if I'm way off in my reasoning. Your thoughts?