Note: There is a potential for confusion in the wording of a constant rate
of snow, but this has no bearing on the problem *unless* you let yourself
be confused by it. We pretend that the height of the snow accumulation is
proportional to the time since it started snowing. But what do we mean by
`height'? Suppose the weather forcast tells us it snowed 5 inches yesterday,
and it will snow another 5 inches today, and no snow melts or gets removed,
and no snow was there before yesterday. Does this mean we have 10 inches
of snow by the end of today? Let us understand the definition of height
in such a way that the answer is yes! If you measure with a ruler, the
ruler might say `no', because the new snow compresses the old snow. But
we don't care what the ruler says, we care what the snowplow says.
And the snowplow has to remove 10 inches worth of snow, even if they got
compressed a bit by settling.