SOLUTION: the speed of an airplane in still air is 224km/h. the plane travels 716 km against the wind and 1904 km with the wind in a total time of 12 hr. what is the speed of the wind?

Question 82011: the speed of an airplane in still air is 224km/h. the plane travels 716 km against the wind and 1904 km with the wind in a total time of 12 hr. what is the speed of the wind?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
distance(d)=rate(r) times time(t) or d=rt;t=d/r and r=d/t
Let r=speed of the wind
time airplane traveled against the wind=716/(224-r)
time airplane traveled with the wind =1904/(224+r)
Now we are told that the sum of these times is 12 hrs. So:
716/(224-r)+1904/(224+r)=12 multiply each term by (224-r)(224+r) to get rid of fractions:
716(224-r)(224+r)/(224-r)+1904(224-r)(224+r)/(224+r)=12(224-r)(224+r) simplify:
716(224+r)+1904(224-r)=12((224-r)(224+r) get rid of parens
160384+716r+426496-1904r=602112-12r^2 simplify
586880-1188r=602112-12r^2 subtract 602112 and add 12r^2 to both sides
12r^2-1188r-15232=0 divide each term by 4
3r^2-297r-3808=0 quadratic in standard form. Solve using quadratic formula:

mph----------------------speed of the wind
discount the negative value of x
CK
716/(224-110.4883)+1904/(224+110.4883)=12
716/(113.5116)+1904/(334.4883)=12
6.3077+5.6923=12
~12=12
----a nasty problem with respect to manipulating the terms---there may be an easier way, but I don't see it. It's good that we have calculators!

Hope this helps----ptaylor

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