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?

Step 1

As a first step, let's convert the given information in a diagram. Please see the white board.

Let A be the point where you are standing. Let B be the position of the locomotive when it passes you and C be the position at which you catch the tail of the train. CD = length of the train.

Step 2

Note that triangle ABC is a right angled triangle. AB = 1/5; BC = x

Please see the white board.

Step 3

Time taken by the train to cover BD = Time taken by you to cover AC

Hence, BD / sp...

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