The speed of an airplane in still air is 214mph The plane tr

The speed of an airplane in still air is 214mph. The plane travels 819mi against the wind and 1505 mi with the wind in a total time of 12 hrs. what is the speed of the wind?

Solution

Let \"w\" be the speed of the wind.
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Against the wind DATA:
distance=819 miles ; Rate=(214-w); time= d/r=819/(214-w) hrs
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With the wind DATA:
distance=1505 miles ; rate=(214+w); time = d/r 1505/(214+w) hrs
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EQUATION:
time + time = 12 hrs
819/(214-w) + 1505/(214+w) = 12
819(214+w) + 1505(214-w)= 12(214^2-w^2)
(2324)(214)+(819-1505)w = 12(45796)-12w^2
12w^2-686w-52216=0
6w^2-343w-26108=0
w=[343+-sqrt(343^2-4*6*-26108]/12
w=[1205.69]/12
w=100.47 mph (speed of the wind)