Schmendreck wrote:With this i get that the snow plow leaves about an hour and 5 minutes after it starts snowing.
I get the same result (with the help of Wolfram|Alpha to get the root of the horrible degree-7 polynomial you end up with... I'd gotten the horrible polynomial, but figured there had to be a better way, until I read your PDF, saw that was the right way, and plugged it into Alpha).
It really should be stated in the question though, how the speed of the plow changes... I mean, assuming that the rate of snow moved by the plow is a constant (ie the speed of the plow is inversely proportional to the height of the snow) is all well and good, but it's just an assumption... it should be in the question. It seems a bit silly to assume that if it had left at 5AM instead of 6AM (when it had only been snowing for 5 minutes) it'd be initially moving at just over 88 miles an hour (maybe they did, and it travelled forward in time to 6AM?)
Is this really a differential equation, though? I mean, we find x'(t) in terms of t, and find x(t)... that's just integration. I thought differential equations were finding x'(t) in terms of x(t) and possibly t (or similar for higher orders)... Just a difference of terminology?