Big Red, a veteran pilot and jack-of-alltrades, took a break from his summer chores to analyze his upcoming busy season when he’d make hundreds of worldwide deliveries. Red, who considered himself the king of just-in-time supply, reviewed his flight patterns from years past, verifying the efficiency of his routes.
He determined that for his stops in the tropics, he should take the shortest distance from his headquarters south to the equator, unload some cargo, then head due west to his next equator stop, before returning home on a northbound flight. According to his calculations, the north and southbound legs should be exactly the same distance.
How could Red possibly end up back home without ever traveling east? And, if the area enclosed by this flight pattern makes up 10% of the earth’s surface, how far would he travel due west along the equator?
Remember, the Earth is round. Let’s say it’s perfectly spherical and has an exact radius of 4,000 miles.