# Burning down the house

Use the conservation equation to find $$\langle s\rangle$$ in terms of $$\rho_\textrm{tree},$$ $$f,$$ and $$r.$$

What is $$\langle s\rangle$$ when $$\rho_\textrm{tree} = 0.4,$$ $$f = 0.01,$$ and $$r = 0.05?$$

Hint: Recall that $$\rho_\textrm{empty} + \rho_\textrm{tree} + \rho_\textrm{burning} = 1.$$

Assume that $$\rho_\textrm{burning} \ll \{\rho_\textrm{empty}, \rho_\textrm{tree}\}.$$

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