[heelix]

Suspect they were IFR. All your points stand. First time flying things with a jet engine, I was shocked how much more fuel gets burned at low altitude. It almost always works out better to max climb to altitude and descend than to fly low and level. On a small jet, things can get spicy fast when ATC route you around at 5000' for 15 minutes or so. Three aborted landings would gobble gas like crazy.

§ 91.167 Fuel requirements for flight in IFR conditions.

(a) No person may operate a civil aircraft in IFR conditions unless it carries enough fuel (considering weather reports and forecasts and weather conditions) to—

(1) Complete the flight to the first airport of intended landing;

(2) Except as provided in paragraph (b) of this section, fly from that airport to the alternate airport; and

(3) Fly after that for 45 minutes at normal cruising speed

[raviolo]

They were most definitely IFR. Not because of the weather but because IFR is required above certain altitude 18,000 ft in the U.S. and typically lower in Europe (depends on a country). Jets including small private jets are almost always on IFR. Airliners with passengers - always.

[mr_00ff00]

Why does it burn fuel so fast?

[TZubiri]

My guess is higher air density means more wind resistance, which acts as negative forward acceleration.