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Let a be the speed of the column, b the speed of the officer, and x be the the length of the column. Let t' be the time for the officer to reach the front of the column and t be the total time. We then get the following relationships:
at = x
bt' = at' + x
bt = 2at' + x
Do a bunch of algebra and get b/a = 1+sqrt(2)
Let me know if it isn't working out.
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