The Snowplow Problem
To apply the techniques discussed in this chapter to real-worldproblems, it is neces-
sary to translate these problems into questions that can beanswered mathematically.
The process of reformulating a real-world problem as amathematical one often requires
making certain simplifying assumptions. To illustrate this,consider the following snow-
plow problem:
One morning it began to snow very hard and continued snowingsteadily
throughout the day. A snowplow set out at 9:00 am to clear aroad,
clearing 2 mi by 11:00 am and an additional mile by 1:00 pm. Atwhat
time did it start snowing?
To solve this problem, you can make two physical assumptionsconcerning the rate
at which it is snowing and the rate at which the snowplow canclear the road. Because
it is snowing steadily, it is reasonable to assume it is snowingat a constant rate. From
the data given (and from our experience), the deeper the snow,the slower the snowplow
moves. With this in mind, assume that the rate (in mph) at whicha snowplow can clear
a road is inversely proportional to the depth of the snow.
please show all work
