Most Ridiculous Routes

A postman with time to spare, made a point of finishing his round by walking as far as possible while visiting his last ten houses, which were equally spaced on a straight road.  Assuming a distance of 1 unit between each house, what is the longest distance he could walk, starting at house 1 and visiting each other house once? What if he started at house 2? 3? 4? 5?

Source: Based on The Penguin Book of Curious and Interesting Puzzles, David Wells, #535.


Solution
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