SOLUTION: A plance travels 2100 km with the wind. The return trip against the wind is 1 h longer. If the rate of the plane in still air is 325 km/h, find the rate of the wind.

Question 535921: A plance travels 2100 km with the wind. The return trip against the wind is 1 h longer. If the rate of the plane in still air is 325 km/h, find the rate of the wind.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Plane speed = 325
wind speed = x

Speed with wind 325 + x
Speed against wind 325 - x

Distance = 2100 km

t=d/r

Time against wind - Time with Wind = 1
2100 /( 325-x)- 2100/(325+x ) = 1
LCD= ( 325 - x)( 325 + x)
Multiply equation by LCD
We get
2100 ( 325+x)- 2100(325-x)=1*(325-x)(325+x)
682500+2100x -682500+2100x=1*( 105625 -x^2)
4200 x =105625 -1x^2
-1 x^2 -4200 x + 105625 = 0
Find the roots of the equation by quadratic formula

a= -1 ,b= -4200 c 105625

b^2-4ac= 17640000 - 422500
b^2-4ac= 18062500
= 4250

x1=( 4200 + 4250 )/ -2
x1= -4225
x2=( 4200 -4250 ) / -2
x2= 25
Ignore negative value
speed = 25 mph
m.ananth@hotmail.ca

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