SOLUTION: A plane flies 600 miles against a steady 25mph headwind and then returns to the same point with the wind. If the trip takes 10 hours what is the planes speed while still in the ai

Question 524819: A plane flies 600 miles against a steady 25mph headwind and then returns to the same point with the wind. If the trip takes 10 hours what is the planes speed while still in the air?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
plane speed x mph
wind speed 25 mph

Distance with wind 600 miles
Distance against wind 600 miles

spee with wind x + 25 mph
speed against x -25 mph
Total time = 9 hours
Time with current= 600 /( x + 25 )
time against current 600 / ( x -25 )

Time with current + time against = 10 hours

600 /( x + 25 ) + 600 /(x -25 ) = 10
LCD = ( x + 25 )* (x -25 )
multiply the equation by the LCD
we get
600*(x-25)+600(x+25)=10(x^2-625 )
600x-15000+600x+15000=10X^2-6250
1200x=10x^2-6250
10X^2-1200x-6250=0
10x^2-1200x-6250=0
/ 10
x^2 -120 x -625 = 0
x^2-125x+5x-625=0
x(x-125)+5(x-125)=0
(x+5)(x-125)=0
x= 125 speed of plane
negative is ignored. speed cant be negative

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