Out for a hike

Suppose that to hike a distance \(L\) while carrying nothing, your body requires an amount \(L \gamma_0\) of food, and that when you carry an extra weight \(M\) in your backpack, your body is less efficient and requires the amount of food \[L \gamma_0 \left(1+\frac{M}{W_\text{body}}\right)\] where \(W_\text{body}\) is the weight of your body.

If you start out with the weight \(M\) of food in your ultralight (weightless) backpack, how far (in miles) can you hike in total?


  • All your energy comes from eating the food in your backpack.
  • You eat the food as needed for your energy needs.
  • \(M=\SI{50}{lb}\), \(W_\text{body}=\SI{160}{lb},\) \(\gamma_0=12^{-1}\si{lb\ food\ per\ mile}.\)
  • American pack weights are measured in pounds, which are equivalent to roughly \(\SI{0.454}{\kilo\gram}.\)

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