Suppose you are standing in a field near a straight section of railroad tracks just as the locomotive of a train passes the point nearest to​ you, which is 1/5 mi away. The​ train, with length 1/12 mi, is traveling at 13 mi/hr. If you start running in a straight line across the​ field, how slowly can you run and still catch the​ train? In which direction should you​ run?   Let v be your velocity and let x be the difference between the position of the locomotive when it passes you and the position at which you catch the tail of the train. What is the objective function in terms of​ x?

Question
Suppose you are standing in a field near a straight section of railroad tracks just as the locomotive of a train passes the point nearest to​ you, which is 1/5 mi away. The​ train, with length 1/12 mi, is traveling at 13 mi/hr. If you start running in a straight line across the​ field, how slowly can you run and still catch the​ train? In which direction should you​ run?
 
Let v be your velocity and let x be the difference between the position of the locomotive when it passes you and the position at which you catch the tail of the train. What is the objective function in terms of​ x?

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