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Stu Hears That Whistle A-Blowing....

Although warned of the danger numerous times, Stu Dent always walked across the railroad bridge on his way to school. One day, Stu was one-fourth of the way across the bridge when he heard a train approaching from behind him. It was exactly one bridge-length away from him. Which direction should he run...back or forward?

Note: Could you generalize your solution for the case where Stu is 1/n-th of the way across the bridge?

 


Hint: Use d = rt to set up two equations, one for each direction he could run.

 


Solution Commentary: Suppose B = length of bridge, R = rate of train, XT = Stu's speed needed to escape running towards the train, and AT = Stu's speed needed to escape running away from the train.

Then, if Stu runs towards the train, (B/4)/XT = (3B/4)/S.

And, if Stu runs away from the train, (3B/4)/AT = (7B/4)/S.

Then.....