AdamFrisch - Has raised the important point that what we need to do is minimise drag in order to get max endurance and that this is achieved at Vbg or Vy. This will vary with weight but if,as AtoBsafely has suggested, we assume 2/3 of the original fuel, we won't be far off.
AtoBSafely has raised the point that we would be more efficient operating on one engine at a higher power than two engines at lower power. Would the additional drag caused by asymmetric flight outweigh the advantage and would the on-board systems feed all the fuel to the one running engine without further intervention?
AdamFrisch has also suggested that endurance is independent of altitude. Instinctively this sounds right - maybe someone can comment on whether fuel flow varies for a given KTAS (approx Vy) at different altitudes.
So the question may boil down to - what is the fuel burn, independent of altitude, on a single engine, to fly at Vbg (or Vy)at approx 2/3 of the original fuel load? Given that we start with 43,800 kg of fuel, how long will this last?
Gentlemen;
1. Re "AdamFrisch". Max endurance will not necessarily be at least drag for a 777. Max endurance will be at minimum fuel flow, and minimum fuel flow will be a function of not only drag, but engine thrust per pound of fuel consumed.
2. Re operating on one engine vice 2; it may be possible at low altitudes for a jet to have more endurance (less fuel flow on one than two), but I have not seen any numbers to suggest that this can be true at higher altitudes
3. max endurance (time) is certainly not independent of altitude. As I said earlier, the thrust specific fuel consumption is much higher at lower power settings than higher ones, hence higher power settings will give more thrust per pound of fuel burned. Caveat, I use the term "high power settings" to indicate those not far below maximum N1.