First read T&Cs of the journey!
Let's assume that the only airport mentioned is located at the top of the earth.
Recollect all the data given.
----------------------------------------------------------------------------
1. The professor's plane must make a single continuous trip around the world without landing or turning around.
2. Each plane can travel exactly 1 degree of longitude in 1 minute
for every kiloliter of fuel. Each can hold a maximum of 180 kiloliters
of fuel.
3. Any plane can refuel any of the others in mid-air by meeting at the same point and instantly transferring any amount of fuel.
4. Fugari and Orokana's planes can turn around instantaneously without burning fuel.
5. Only one airport is available for any of the planes to land, take off, or refuel.
6. All three planes must survive the experiment, and none may run of fuel in mid-air.
------------------------------------------------------------------------------
As per (2), since each plane travel 1 degree of longitude in 1 minute for every kiloliter of fuel, means that plane need 360 minutes (6 hours) and 360 kiloliters of fuel. But remember plane can hold only 180 kiloliters
of fuel.
Let's suppose that, all three planes takes off from airport exactly at 12:00 PM towards the WEST.
We will break this 6 hours journey into 8 parts where each plane travels 45 degree of longitude east or west using 45 kiloliters of fuel.
START :
--------------------------------------------------------------------------------
PART 1 :
Exactly at 12:45 PM, all will be at 45 degree angle with reference to the center of the earth.
At this point, each of them will use 45 kiloliters of fuel. Hence, each will have 135 kiloliters of fuel. Here, Orokana gives away 45 kiloliters to each of Fukano & Fugari. So she is left with the 45 kiloliters which she uses to go back to the starting point.
---------------------------------------------------------------------------------
PART 2 :
In next 45 minutes, both Fukano and Fugari moves to 90 degree of longitude spending 45 kiloliters of fuel. Now,here both will have 135 kiloliters each in their fuel tank. Here, Fugari refuels Fukano's fuel tank with 45 kiloliters of fuel; leaving 90 kiloliters in own tank for the backward journey towards the starting point.
---------------------------------------------------------------------------------
PART 3 :
Fukano travels further, while Fugari is in midway of the backward journey. Again, both spend 45 kiloliters of fuel.
----------------------------------------------------------------------------
PART 4 :
Exactly at 3:00 PM, Fukano reaches at 180 degree while Fugari reaches back to the starting point. Till then, Orokana refuels her plane & takes off towards EAST. She has to take off as Fukano is left with only 90 kiloliters of fuel by which he could travel half of the rest of journey.
-----------------------------------------------------------------------------
PART 5 :
In next 45 minutes, Fukano's plane uses 45 kiloliters further while Orokana travels 1/3rd of Fukano's remaining journey in reverse direction so as to meet Fukano in midway. In process, her plane again uses 45 kiloliters of fuel with 135 kiloliters left.
--------------------------------------------------------------------------------
PART 6 :
At 04:30 PM, Orokana meets Fukano whose plane had no fuel left at the point & refuels his plane with 45 kiloliters of fuel. Remember Orokana's plane consumed 45 kiloliters more till she meets Fukano. Now, since both of them have left only 45 kiloliters in fuel tank, Fugari whose plane standing at airport is refueled at full 180 kiloliters takes of in the direction of EAST.
----------------------------------------------------------------------------------
PART 7 :
At 05:15 PM, when fuel tank indicators of both Fukano & Orokana are pointing to 0, Fugari meets them & gives 45 (to Fukano) + 45 (to Orokana) = 90 out of 135 (180 - 45 used since take off) . Now all are left with 45 kiloliters of fuel & 45 degrees of journey is left.
----------------------------------------------------------------------------------
PART 8 :
And this is how, exactly at 06:00 PM all of them reaches back to the starting point safely.
But is this the most efficient way to make trip around the Earth? Certainly not!
If plane was built with fuel tank of 360 + then the mission wouldn't have required any assistance. Just because of limited fuel tank, 45 + 45 + 90 + 90 + 90 + 90 + 45 + 45 = 270 Kiloliters of fuel burnt to assist Fukano's plane.
