SOLUTION: an airplane flies 150 miles east, then returns to the beginning point. The total flight time is 2 hours. The flight to the east is with the wind, and the return trip is against t

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Question 864657: an airplane flies 150 miles east, then returns to the beginning point. The total flight time is 2 hours. The flight to the east is with the wind, and the return trip is against the wind. The wind is blowing at 25 miles per hour. What is the speed of the plane with no wind, to the nearest tenth?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Plane speed x mph Time forward + time return = hours 2 hours
wind speed 25 mph

against wind x- 25 mph
with wind x+ 25 mph

Distance= 150 miles

Time against + time with = 2 hours
t=d/r

150 /( x + 25 ) + 150 /(x - 25 ) = 2

LCD = (x - 25 ) ( x + 25 )
150 *( x - 25 ) + 150 (x + 25 ) = 2 (x^2 - 625 )
150 x - -3750 + 150 x + 3750 = 2 ( x ^2 - 625 )
300 x = 2 x ^2 -1250
2 x ^2 - -300 x - 1250 = 0

Find the roots of the equation by quadratic formula

a= 2 , b= -300 , c= 1250

b^2-4ac= 90000 + -10000
b^2-4ac= 80000
%09sqrt%28%0980000%09%29=%09282.84%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=( 300 + 282.84 )/ 4
x1= 145.71
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 300 -282.84 ) / 4
x2= 4.29

Plane speed 145.7 mph

m.ananth@hotmail.ca