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jdlandreth Group Title

you, in your new red Porsche, decide to make a 160km trip to Carolina Beach, traveling at 80km?hr. Your make a return trip at a rate of 48km?hr. What was your average speed for the entire trip?

  • one year ago
  • one year ago

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  1. satellite73 Group Title
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    figure out the total time, and the total distance divide the total distance by the total time

    • one year ago
  2. satellite73 Group Title
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    ok it was easy but i got it wrong total distance is \(2\times 160=320\)

    • one year ago
  3. satellite73 Group Title
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    time going in your new red porche is \(\frac{160}{80}=2\)

    • one year ago
  4. satellite73 Group Title
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    how about the time returning?

    • one year ago
  5. jdlandreth Group Title
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    ugh i don't know cause it comes out as a decimal?

    • one year ago
  6. satellite73 Group Title
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    much easier (believe it or not) if you leave it as a fraction

    • one year ago
  7. satellite73 Group Title
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    in other words, take \(\frac{160}{48}\) and instead of writing it as a repeating decimal, reduce it to \(\frac{10}{3}\)

    • one year ago
  8. satellite73 Group Title
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    so far so good?

    • one year ago
  9. jdlandreth Group Title
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    okay so? then do i leave the other as 2? or 160/2?

    • one year ago
  10. satellite73 Group Title
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    no use 2

    • one year ago
  11. satellite73 Group Title
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    now the next job is to total up the time, in other words compute \[2+\frac{10}{3}\] leave it as a fraction

    • one year ago
  12. jdlandreth Group Title
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    okay then what?

    • one year ago
  13. jdlandreth Group Title
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    16/3

    • one year ago
  14. satellite73 Group Title
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    right and now speed is distance divided by rate

    • one year ago
  15. satellite73 Group Title
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    so your final job is \[320\div \frac{16}{3}\]

    • one year ago
  16. jdlandreth Group Title
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    So the average is 60?

    • one year ago
  17. satellite73 Group Title
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    that is what i get too

    • one year ago
  18. jdlandreth Group Title
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    kay good. Thank you!!

    • one year ago
  19. satellite73 Group Title
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    notice two things 1) the average speed is not the "average of the speeds" and 2) the 160 is a red herring if you really want to impress your math teacher, show that it works no matter how far you drive

    • one year ago
  20. satellite73 Group Title
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    you could drive 160 miles or 100 miles or 3,000 miles or \(m\) miles, the average will still be 60

    • one year ago
  21. jdlandreth Group Title
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    Okay Thank you soo much. =)

    • one year ago
  22. satellite73 Group Title
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    yw

    • one year ago
  23. satellite73 Group Title
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    try it with \(m\) you get \[\frac{2m}{\frac{m}{80}+\frac{m}{48}}=60\] after some algebra

    • one year ago
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