Precalculus 11
posted by Kayla
Hello,
An airplane makes a 990 km flight with a tailwind & returns, flying into the same wind. The total flying time is 3 hrs 20 mins & the airplanes speed in still air is 600 km/hr what is the the speed of the wind?
I'm as far as (990/(600x))+(990/600+x))=10/3
but I can't figure out how to go from there!
Thanks a bunch :)
Kayla

bobpursley
same distance, there and back
v1*t1=v2*t2=990km
t1=3 1/3 hr t2
v1=600+w
v2=600w
(600+w)t1=990 or
t1=990/(600+w)
10/3t1=990/(600w)
10/3990/(600+w) = 990/(600w) so your equation is correct.
now, multipy each side by (600w)(600+w)/990
10(600^2w^2)/(3*990) = 600+w+600w)
check that. Now is simplifies considerably, gather terms, and you have a quadratic equation. use the quadratic formula. 
scott
multiply by the LCD
[990 (600 + x)] + [990 (600  x)] = 10/3 (600  x)(600 + x)
1188000 = 10/3 (360000  x^2) ... 356400 = 360000  x^2
x^2 = 3600
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