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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
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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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1They 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
 one year ago
Best ResponseYou've already chosen the best response.1And we want to figure out uhhhh, 16 knots in 1 hour.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Solving it is easy, I'm just trying to think of the correct equation they want to see hehe.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it 97280 feet? 6080 times 16?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Yes, simple as that! :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cool, yea idk what equation they wanna see either lol could it just be 6080(16) = x or something?

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

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1How bout part b, any ideas? c:

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i have no idea about that one lol

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1So 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
 one year ago
Best ResponseYou've already chosen the best response.1Let's call that unknown amount, x.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1So,\[\Large\rm \frac{97280ft}{hr}=\frac{x~mi}{hr}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1The units on the bottom are the same, we'll get rid of those, ignore them.\[\Large\rm 97280ft=x~mi\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1What next, how do we solve for x? c: What do you think?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0uhh divide 97280 by 16?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1That 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
 one year ago
Best ResponseYou've already chosen the best response.0sorry i'm not really sure about this one, would be it to divide it by 6080?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1I 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
 one year ago
Best ResponseYou've already chosen the best response.06080 divided by 97280? which is 0.0625?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Noo 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
 one year ago
Best ResponseYou've already chosen the best response.0oh so 97280 divided by 5280 = 18.42?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ok good job \c:/ So we figured out that `16knots per hour` is equivalent to `18.42miles per hour`
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