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## Homework Statement

I am trying to model using differential equations rain falling from the sky, hitting the pavement, and then running off the pavement into the ground. I'm a little rusty on differential equations and I'm just wondering if my answer is correct. In this model I'm assuming that the rain is only landing on the pavement, not on the ground around the pavement. I'm also assuming that the source of the rain will never run out.

## The Attempt at a Solution

[itex]\frac{dS}{dt}[/itex]=c-P-G

[itex]\frac{dP}{dt}[/itex]=P-G

[itex]\frac{dG}{dt}[/itex]=-S-P

[itex]\frac{dS}{dt}[/itex] is the amount of rain in the sky per unit time

[itex]\frac{dP}{dt}[/itex] is the amount of rain on the pavement per unit time

[itex]\frac{dG}{dt}[/itex] is the amount of rain on the ground per unit time

c is the constant source of rain

P is the rain on the pavement

G is the rain on the ground

S is the rain in the sky

Does this look correct or is it completely off? Thanks!