SOLUTION: The speed of an airplane still in the air is 203 km/hr. The plane travels 666 km against wind and 769 km with the wind in a total time of 11 hours. What is the speed of the wind (k

Algebra ->  Radicals -> SOLUTION: The speed of an airplane still in the air is 203 km/hr. The plane travels 666 km against wind and 769 km with the wind in a total time of 11 hours. What is the speed of the wind (k      Log On


   

Question 548516: The speed of an airplane still in the air is 203 km/hr. The plane travels 666 km against wind and 769 km with the wind in a total time of 11 hours. What is the speed of the wind (km/hr.)?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
plane speed = 203 km/h
wind speed = x km/h
against wind = 203 - x
with wind = 203 + x
Total Time= 11.00 hours
Time against + time with = 11
666/(203-x)+769 /(203+x )=11
666(203 +x)+769(203-x)= 11
135198+666x+156107-769x =11(203^2-x^2)
135198+666x+156107-769x =453299-11x^2
11x^2-103x-161994=0
Find the roots of the equation by quadratic formula

a=11 ,b=-103 ,c=-161994

b^2-4ac= 10609 + 7127736
b^2-4ac= 7138345
%09sqrt%28%097138345%09%29=%092671.77%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 103 + 2671.77 )/ 22
x1= 126.13
x2=( 103 -2671.77 ) / 22
x2= -116.76
Ignore negative value
wind speed 126.13 mph