?Snow began to fall during the morning of February 2 and continued steadily into the

Chapter 16, Problem 8

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Snow began to fall during the morning of February 2 and continued steadily into the afternoon. At noon a snowplow began removing snow from a road at a constant rate. The plow traveled  from noon to  but only  from  to . When did the snow begin to fall? [Hints: To get started, let  be the time measured in hours after noon; let  be the distance traveled by the plow at time ; then the speed of the plow is . Let  be the number of hours before noon that it began to snow. Find an expression for the height of the snow at time . Then use the given information that the rate of removal  (in  ) is constant.]

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