# 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?

Assumptions

• All your energy comes from eating the food in your backpack.
• You eat the food as needed for your energy needs.
• $$M$$ = 50 lb
• $$W_\text{body}$$ = 160 lb
• $$\gamma_0=12^{-1}$$ lb food per mile
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