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Ds or d/2 * 2s

  1. Sep 15, 2011 #1
    which is greater or are they equal

    1) the time required to travel d miles at s miles per hour

    or

    2) the time required to travel d/2 miles at 2s miles per hour


    I thought 1) is equivalent to d*s or ds

    and I thought 2) is equivalent to

    d/2 * 2s

    which simplifies to

    ds

    so they're the same but my book says 1) is greater
     
  2. jcsd
  3. Sep 15, 2011 #2

    pwsnafu

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    Suppose Adam travels at 10 mph. He wants to travel 40 miles. How long will it take him?
    Suppose Bob travels 20 mph. He wants to travel 20 miles. How long will it take him?
     
  4. Sep 15, 2011 #3

    cepheid

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    Staff Emeritus
    Science Advisor
    Gold Member

    The problem you're having here is that the time required to travel distance d at speed s is d/s, not d*s.
     
  5. Sep 15, 2011 #4

    Mentallic

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    Homework Helper

    d/s = t, so rearranging this we get d = st

    If the options were instead:

    1) the distance traveled after t hours at s miles per hour

    2) the distance traveled after t/2 an hour at 2s miles per hour

    Then they would be equal, because using the rearranged equation we have

    1) d = s*t
    2) d = 2s*t/2 = s*t

    Oh and by the way, to remember this equation, it should just be intuitive but if you can't do that, think about the units! Distance is measured in miles (or equivalent), time is measured in hours, and speed is measured in miles/hour. So from this you can quickly tell that speed = distance / time since miles per hour means miles / hours.
     
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