anonymous
  • anonymous
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
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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zepdrix
  • zepdrix
They gave us some information, this\[\Large\rm \color{royalblue}{N=6080ft}\]and this, \[\Large\rm \color{orangered}{1knot=\frac{1\color{royalblue}{N}}{hr}}\]
zepdrix
  • zepdrix
And we want to figure out uhhhh, 16 knots in 1 hour.
zepdrix
  • zepdrix
Solving it is easy, I'm just trying to think of the correct equation they want to see hehe.

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anonymous
  • anonymous
is it 97280 feet? 6080 times 16?
zepdrix
  • zepdrix
Yes, simple as that! :)
anonymous
  • anonymous
cool, yea idk what equation they wanna see either lol could it just be 6080(16) = x or something?
zepdrix
  • zepdrix
\[\Large\rm 16(1knot)=16\left(\frac{1N}{hr}\right)\]\[\Large\rm 16knot=\frac{16N}{hr}\]\[\Large\rm 16knot=\frac{16\cdot6080ft}{hr}\]\[\Large\rm 16knot=\frac{97280ft}{hr}\]And since it was a duration of 1 hour, we want that entire value. Ya ya something like that maybe :3
zepdrix
  • zepdrix
How bout part b, any ideas? c:
anonymous
  • anonymous
i have no idea about that one lol
zepdrix
  • zepdrix
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.
zepdrix
  • zepdrix
Let's call that unknown amount, x.
zepdrix
  • zepdrix
So,\[\Large\rm \frac{97280ft}{hr}=\frac{x~mi}{hr}\]
zepdrix
  • zepdrix
The units on the bottom are the same, we'll get rid of those, ignore them.\[\Large\rm 97280ft=x~mi\]
zepdrix
  • zepdrix
What next, how do we solve for x? c: What do you think?
anonymous
  • anonymous
uhh divide 97280 by 16?
zepdrix
  • zepdrix
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
anonymous
  • anonymous
sorry i'm not really sure about this one, would be it to divide it by 6080?
zepdrix
  • zepdrix
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? :)
anonymous
  • anonymous
6080 divided by 97280? which is 0.0625?
zepdrix
  • zepdrix
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? :)
anonymous
  • anonymous
oh so 97280 divided by 5280 = 18.42?
zepdrix
  • zepdrix
Ok good job \c:/ So we figured out that `16knots per hour` is equivalent to `18.42miles per hour`
anonymous
  • anonymous
thank you!
zepdrix
  • zepdrix
npppp

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