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anonymous

  • one year ago

On the sea, distances are measured in nautical miles rather than miles. 1 nautical mile = 6080 feet and 1 knot = 1 nautical mile/hour a. If a boat travels 16 knots in 1 hour, how far will it have traveled in feet? Write and solve an equation. b. About how fast was the boat traveling in miles per hour? Round your answer to the nearest hundredth. @zepdrix

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  1. zepdrix
    • one year ago
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    They gave us some information, this\[\Large\rm \color{royalblue}{N=6080ft}\]and this, \[\Large\rm \color{orangered}{1knot=\frac{1\color{royalblue}{N}}{hr}}\]

  2. zepdrix
    • one year ago
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    And we want to figure out uhhhh, 16 knots in 1 hour.

  3. zepdrix
    • one year ago
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    Solving it is easy, I'm just trying to think of the correct equation they want to see hehe.

  4. anonymous
    • one year ago
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    is it 97280 feet? 6080 times 16?

  5. zepdrix
    • one year ago
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    Yes, simple as that! :)

  6. anonymous
    • one year ago
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    cool, yea idk what equation they wanna see either lol could it just be 6080(16) = x or something?

  7. zepdrix
    • one year ago
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    \[\Large\rm 16(1knot)=16\left(\frac{1N}{hr}\right)\]\[\Large\rm 16knot=\frac{16N}{hr}\]\[\Large\rm 16knot=\frac{16\cdot6080ft}{hr}\]\[\Large\rm 16knot=\frac{97280ft}{hr}\]And since it was a duration of 1 hour, we want that entire value. Ya ya something like that maybe :3

  8. zepdrix
    • one year ago
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    How bout part b, any ideas? c:

  9. anonymous
    • one year ago
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    i have no idea about that one lol

  10. zepdrix
    • one year ago
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    So we've found our speed in knots, 97280 feet per hour. We know that this is equivalent to `some amount` of miles per hour.

  11. zepdrix
    • one year ago
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    Let's call that unknown amount, x.

  12. zepdrix
    • one year ago
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    So,\[\Large\rm \frac{97280ft}{hr}=\frac{x~mi}{hr}\]

  13. zepdrix
    • one year ago
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    The units on the bottom are the same, we'll get rid of those, ignore them.\[\Large\rm 97280ft=x~mi\]

  14. zepdrix
    • one year ago
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    What next, how do we solve for x? c: What do you think?

  15. anonymous
    • one year ago
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    uhh divide 97280 by 16?

  16. zepdrix
    • one year ago
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    That would tell us how many feet are in 1 knot. Hmm, I don't think that helps us. Notice that the left side of the equation is in `feet`, while the right side is being measured in `miles`. Is there something we can do about that? :o

  17. anonymous
    • one year ago
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    sorry i'm not really sure about this one, would be it to divide it by 6080?

  18. zepdrix
    • one year ago
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    I should have left the hours in the bottom I think. They want the final answer in terms of miles/hour, maybe it's making things more confusing without them. So our equation looks like this:\[\Large\rm 97280\frac{ft}{hr}=x~\frac{\color{orangered}{mi}}{hr}\]Our 16 knots, which is 97280 feet per hour, is equivalent to some amount of miles per hour. We want to change our right side to be in terms of `feet per hour` so the units will match. How many feet in a mile? :)

  19. anonymous
    • one year ago
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    6080 divided by 97280? which is 0.0625?

  20. zepdrix
    • one year ago
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    Noo silly :3 we want the number of feet in a `mile` for this part. Not the number of feet in a `nautical mile`. 1 mile = 5280 feet, ya? :)

  21. anonymous
    • one year ago
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    oh so 97280 divided by 5280 = 18.42?

  22. zepdrix
    • one year ago
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    Ok good job \c:/ So we figured out that `16knots per hour` is equivalent to `18.42miles per hour`

  23. anonymous
    • one year ago
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    thank you!

  24. zepdrix
    • one year ago
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    npppp

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