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Points A, B and X form a rougly equilateral triangle.

I need to pull a cart from A to B, and also need to visit X, but I don't need to have the cart with me there. Walking with the cart costs me double the energy of walking without.

To spend as little energy as possible, I think I'd need to pull the cart to somewhere near the middle of the triangle (I will call this point R), leave it there, walk to X and back to the cart, and pull the cart on to B.

How can one calculate where exactly R is?

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    Do _you_ need to start at A and end up at B, or does that constraint apply only to the cart? That is, is a path like A→B→X or X→A→B a valid solution?2011-10-16
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    @IlmariKaronen ABX would be ok, XAB not2011-10-16
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    @Bart: Then, given that the triangle is "roughly equilateral", $A\to B\to X$ is very likely to be a superior solution. (Namely, even $ARBX$ would be shorter than $ARXRB$, and $ABX$ is then just a further optimization).2011-10-16

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