Where Should You Go?Math brain teasers require computations to solve.
In your last adventure, you left a broken-down supply truck in the middle of a desert, near the equator. You and a Desert Patrol Vehicle (DPV) have been airlifted to the disabled truck so you can repair it and bring it back to camp.
Because of recent attacks, the whole area is under a communications blackout. You must return to camp before sunset so that they can visually identify you. If you return after sunset, they will shoot first and ask questions later.
The repairs take longer than expected, and you realise that driving the truck, you cannot make it to your base camp in time. You will have to return to camp in the DPV (which can travel faster) and leave the truck for another day.
Your camp is 500 miles to the south, but there are also two other camps in the area: one is 520 miles west, the other is 480 miles east.
Where should you go to reach a camp before sunset? The DPV can travel 80 mph, and you have plenty of fuel. It is now 12:50 PM and you know that at your base camp, the sun sets at 7:00 PM. One piece of trivia springs to mind: the circumference of earth is about 24900 miles at the equator.
HintThe sun doesn't set at the same time everywhere in a timezone. The earth is about 24900 miles around and there are 24 hours a day, so the time of sunset changes by 1 hour for every 1038 miles you travel east or west at the equator.
AnswerYou need to travel west.
It will take 6 hours and 15 minutes (500 miles / 80 mph) to reach the southern camp, so you would arrive at 7:05 PM which is just after sunset, too late!
It will take 6 hours (480/80) to reach the eastern camp, so you would arrive at 6:50 PM, but the sun will set earlier than at your current location. In fact, the sun will set about 28 minutes earlier (6:32 PM), so you would be way too late.
(480 miles * 1 hr / 1038 miles = 0.46 hr = 28 min)
It will take 6 hours and 30 minutes (520/80) to reach the western camp, so you would arrive at 7:20 PM, but the sun will set later than at your current location. In fact, the sun will set about 30 minutes later (7:30 PM), so you arrive in time.
(520 miles * 1 hr / 1038 miles = 0.50 hr = 30 min)
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