Flying Around the World
You’ve designed an incredibly advanced aircraft, a true marvel of aeronautics, the X-100. You want to fly all the way around the world in it without stopping. The only problem is that the plane can carry just enough fuel to make it halfway around the Earth.So you build a total of three planes, one for you to fly and two more for your assistants John and Jane. You equip these planes with some pretty incredible and futuristic features to help you along the way. For one, they can instantaneously transfer any amount of fuel to each other. One plane can even pass fuel to the other two simultaneously. Secondly, the aircraft can turn on a dime, literally reversing direction instantaneously, flying at the exact same velocity as soon as they about-face.
Now for the numbers: Each plane can carry 180 gallons of fuel. You plan to fly all the way around the world along the equator, where your plane can fly at the blistering speed of 1º of longitude per minute, meaning it’ll take 360 minutes to make the whole 360-degree journey. (This is a speed of about Mach 5.4, for those who are curious). The three aircraft burn 1 gallon of fuel per 1º longitude traveled.
One more thing: There is only one airport along the equator route that you plan to take. You must start at this airport and finish there. John and Jane can return to the airport to refuel, filling their tanks to the full 180 gallons. The one airport is the only place that anyone can land.As you can see, with 180 gallons of fuel, one of the planes by itself would only make it 180º around the world, half of the required 360º. Fortunately, the planes have their nifty instantaneous refueling and about-facing features, and you have John and Jane to help you make the trip.How do you fly all the way around the world without stopping or turning around, and without any of the three pilots running out of fuel and crashing?
As mentioned, you are probably going to want pencil and paper for this. Draw out a circle representing the world and mark 90º, 180º, 270º and 360º. Imagine you are looking at the south pole and the equator runs along the circumference of the circle. It might help to make a table to keep track of all three planes’ fuel levels as well. Where do the refuelings need to occur for you to make it all the way around in one continuous trip?
Note: If a plane hits 0 gallons of fuel, and at that exact moment another plane is there to refuel it, the plane does not crash. The fuel transfers instantaneously.
Before you check out the solution, you should have a piece of paper in front of you with circles and scribbles and cuss words and madness. Then check the answer here.