One cold morning in Calculus City, the residents wake to $8\text{ inches}$ of snow on the ground from the night before.

At 7:00 am, the snow starts to fall again at a rate of:

$$ S(t)={ t }^{ 2 }+t$$

...where $t$ is the number of hours past 7:00 am.

Rita Rates is excited by the snow, but must get to work!

At 8:00 am, she starts shoveling at a rate $R(t)$ given by:

$$ R(t)=3{ t }^{ 3 } $$

How much snow is still on the ground after at 9:00 am when she has to leave?

All rates are measured in inches/hour.