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anonymous
 one year ago
An airplane takes 1 hour longer to go a distance of 816 miles flying against a headwind than on the return trip with a tailwind. If the speed of the wind is 50 miles per hour, find the speed of the plane in still air.
anonymous
 one year ago
An airplane takes 1 hour longer to go a distance of 816 miles flying against a headwind than on the return trip with a tailwind. If the speed of the wind is 50 miles per hour, find the speed of the plane in still air.

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amistre64
 one year ago
Best ResponseYou've already chosen the best response.2you can use distance equations to help solve this

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2distance = speed x time the distance remains constant, the speeds remain constant, its the time and the interaction that vary (a+w) t = d (aw) (t+1) = d

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2w is wind speed, a is airplane speed, at least in my head

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2now using these 2 equations ... we can work up something that with any luck will give us a relationship that we can solve (a+w) t = d (aw) (t+1) = d at wt = d at +a wt w = d a = w(2t+1) but t = d/(a+w) so .. a = w(2d/(a+w)+1) a = 2wd/(a+w) +w a(a+w) = 2wd +w(a+w) a(a+w)w(a+w) = 2wd a^2 +aw aw w^2 = 2wd a^2 w^2 = 2wd a^2 = 2wd + w^2

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2im sure theres a simpler process .... but i can never recall it off hand

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i need to get the a? isn't?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2yes, our goal is to get the speed of the airplane (a)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it's not factorable using factoring.. can i use quadratic formula? but the answer may have square roots

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2i cant readily see a way to remove the time variable ... i keep coming up with solutions that are not a single point.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2lets see how well this plays tho, lets assume it takes t=1 to get there a = 50(3) = 150 150+50 = 200, not 816 so my thought is evidently not correct

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2maybe this makes better sense? dw:1440940969684:dw

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2the h+1 isnt setting right with me

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2do you see any flaws in my thinking? speed = distance/time; example, miles per hour; or, m/h distance = speed x time distance = (total speed) x time distance = (a/h + w/h) x time distance = (a/h  w/h) x (time+1)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2h is equal to 1 time span yes .... (a+50) t = 816 (a50) (t+1) = 816 my first run thru lets a = 290 t = 816/(290+50) = 2.4 and (29050) (3.4) = 816, so it works out as long as the time stated was 2.4 hours but this seems more complicated than what it usually is

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2a^2 = 2wd + w^2 a^2 = 2(50)(816) + (50)^2 = 84100 a = sqrt(84100) = 290 ...

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2i dont spose we have an answer key to check against

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2... how did you get it tho? :)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2if we solve each setup for time, the time component can be eliminated .... t = d/(a+w) t = d/(aw)  1 d/(a+w) = d/(aw)  1 d(aw) = d(a+w)  a^2+w^2 ad wd = ad +wd  a^2+w^2 wd = wd  a^2+w^2 a^2 = 2wd + w^2 is the same thing i got to start with ... so its bound to be good lol

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0same as you pretty much eg from your (a+w) t = d (aw) (t+1) = d you can go \[\implies \frac{d}{aw} = \frac{d}{a+w} + 1\] then x (aw)(a+w) on each side etc
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