Hello,
The depth of the snow increases with the time (t) : h=B*t
The speed is inversely proportional to the depth of snow
v=A/h=A/(Bt)=k/t
==>v=dx/dt)=k/t
In the period of 6 am to 8 am: if T is the time of the begining of the fallen snow:
[tex]1= \int\limits^{T+2}_{T} { \dfrac{k}{t} } \, dt =k*ln( \frac{T+2}{T} )[/tex]
Further,
[tex]1= \int\limits^{T+2+3.5}_{T+2} { \dfrac{k}{t} } \, dt =k*ln( \frac{T+5.5}{T+2} )\\
==\textgreater\ \dfrac{T+5.5}{T+2} = \dfrac{T+2}{T} \\
==\textgreater\ T= \dfrac{4}{1.5} =2+ \dfrac{2}{3} h[/tex]
