Math Problem of the Fortnight: Indiana Jones and the Shortest Crusade
Indiana Jones, having just recovered the Cross of Coronado in the Utah desert, needs to get back to town as soon as possible. He is currently 8 miles west of a railroad track that runs directly north and south; the nearest town is 4 miles east of this track and 10 miles south of Indy’s position.
Running across the desert, Indy can sustain an average speed of 7 miles per hour. There is a circus train traveling south on the railroad track at 21 miles per hour. By the laws of movie physics, the train will be passing by when Indy gets to the tracks, so Indiana can run toward any point on the tracks, jump on the train at that point, ride the train south for a while, then jump off and run the rest of the way to town.
In order to get to the town as quickly as he can, where should Indiana jump on the train, and where should he jump off?
(Assume that the train is short enough that running along the top from car to car cannot shorten Indiana’s time in any significant way. Besides, there are men with guns up there, and rhinoceros horns.)
Rules and guidelines
Winning Solution
The winning solution to this problem was by Rob Brase.
Other correct solutions were by Seth Hoffert, Chris Michener and Nate Stender
