Hike 'til you drop

Calculus Level 3

You're going hiking and need to pack food and water to keep you alive. You have a backpack that carries a certain amount of weight \(W\) and can pack it with any combination of food and water such that \(M_\text{food}+M_\text{water}=W\). Suppose your body requires 50 mL water for each mile that you hike, and that you also need 150 kilocalories of energy for every mile hiked. If the caloric density of your food is \(\gamma_\text{food}\) kcal per gram, what is the furthest distance you can hike (in miles)?


  • \(\gamma_\text{food}\) = 4.62 kcal per gram
  • \(W\) = 15 kg

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