Professor, Foucault know, the famous eccentric scientist and adventurer has embarked on a new challenge flying around the world non-stop in a plane of his own design able to travel consistently at the incredible speed of one degree, longitude around the equator per minute. The plane would take six hours to circle, the world there's, just one problem. The plane can only hold 180 kiloliters of fuel only enough for exactly half the journey let's be honest.
The professor probably could have designed the. Plane to hold more fuel, but where's, the fun in that, instead he's devised a slightly more elaborate solution, building three identical planes for the mission. In addition to their speed, the professor's equipped them with a few other unbelievable features.
Each of the planes can turn on a dime and instantly transfer any amount of its fuel to any of the others in midair without slowing down, provided they're next to each other. The professor will pilot the first plane while his two assistants, foo Lauri. And Otto Hanna will pilot each of the others.
However, only one Airport located on the equator has granted permission for the experiment, making it the starting point, the finish line, and the only spot where the planes can land take off or refuel on the ground. How should the three planes coordinate? So the professor can fly continuously for the whole trip and achieve his dream without anyone running out of fuel and crashing according to the professor's calculations, they should be able to pull it off. By a hair, the key is to maximize the support.
Each assistant provides not wasting a single kiloliter of fuel. It also helps us to think symmetrically. So they can make shorter trips in either direction while setting the professor up for a long unsupported stretch in the middle here's, his solution, all three planes take off at noon flying west. Each fully loaded with a hundred and eighty kiloliters after 45 minutes or one-eighth of the way around each plane has 135 kiloliters left, Otto Hanna gives 45. To the professor and 45 to Hugo t, fully refueling them, both with her remaining 45 Autos Hanna returns to the airport and heads to the lounge for a well-deserved break, 45 minutes later with one quarter of the trip complete the professor and foo Saudi are both at 135 kiloliters again, PhD go T transfers 45 into the professor's tank, leaving himself with the 90.
He needs to return professor Foucault, no stretches and puts on his favorite album, he'll be alone for a while in the meantime, Otto Hanna has. Been anxiously, awaiting, Hugo, Dee's, return, her plane, fully refueled and ready to go as soon as his plane touches the ground. She takes off this time, flying East at this point exactly 180 minutes have passed. And the professor is at the halfway point of his journey with 90 kiloliters of fuel left for the next 90 minutes, the professor and Otto Kaunas planes fly towards each other meeting at the 3/4 mark. Just as the professor's fuel is about to run out. He sees Otto Khan his plane, she gives him 45.
Kiloliters of her remaining 90, leaving them with 45 each, but that's just half of what they need to make it to the airport. Fortunately, this is exactly when Hugo t, having refueled takes off 45 minutes later, just as the other two planes are about to run empty. He meets them at the 315 degree point and transfers 45 kiloliters of fuel to each leaving 45 for himself all three planes land at the airport, just as their fuel, gauges reach zero as the reporters and photographers cheer. The professor promises. His planes will soon be available for commercial flights, just as soon as they figure out how to keep their in-flight meals from spilling everywhere you.