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Math Help - word problem - the snow plough problem?

  1. #1
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    Question word problem - the snow plough problem?

    so far I have derived this general equation dl/dt= amountplowed/( intial snow depth + rate of snowfall*t)
    not sure if it's correct

    One morning in a certain town, it begins to snow steadily. At 8:00am a snowplow sets out t
    ear the highway. It can clear a constant amount of snow per unit time, which means that if th
    ow is twice as deep then the plow will move half as quickly. Suppose that the snow plow clear
    wo miles of the highway by 11:00am, and by 2:00pm it has cleared only another 1 mile.
    1. At what time did it start snowing? (Hint: This is a di erential equations class, so yo
    probably need to write down an appropriate di erential equation to model the situation an
    then solve the di erential equation to evaluate the unknown constants in the equation.)
    2. List explicitly all of the assumptions that you made in order to write down your di erentia
    equation in part (1). State whether each assumption seems realistic to you or not.
    3. Suppose now that a second snowplow starts clearing the same road at 9:00am. Will th
    second snowplow crash into the rst snow plow? If so, when?
    4. Is it possible to avoid a crash if the second snowplow changes the time at which it starts out
    Justify your response.
    Last edited by mr fantastic; October 13th 2011 at 01:01 PM. Reason: Re-titled.
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  2. #2
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    Re: word problem - the snow plough problem?

    Quote Originally Posted by wrongturn12 View Post
    so far I have derived this general equation dl/dt= amountplowed/( intial snow depth + rate of snowfall*t)
    not sure if it's correct

    One morning in a certain town, it begins to snow steadily. At 8:00am a snowplow sets out t
    ear the highway. It can clear a constant amount of snow per unit time, which means that if th
    ow is twice as deep then the plow will move half as quickly. Suppose that the snow plow clear
    wo miles of the highway by 11:00am, and by 2:00pm it has cleared only another 1 mile.
    1. At what time did it start snowing? (Hint: This is a di erential equations class, so yo
    probably need to write down an appropriate di erential equation to model the situation an
    then solve the di erential equation to evaluate the unknown constants in the equation.)
    2. List explicitly all of the assumptions that you made in order to write down your di erentia
    equation in part (1). State whether each assumption seems realistic to you or not.
    3. Suppose now that a second snowplow starts clearing the same road at 9:00am. Will th
    second snowplow crash into the rst snow plow? If so, when?
    4. Is it possible to avoid a crash if the second snowplow changes the time at which it starts out
    Justify your response.
    This question has been posted several times over the years. I suggest you do a Search for it. Also, it would help if you showed what you could do and said where you were stuck.
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