SOLUTION: Kate flew her plane for 6 hours at a constant speed. She traveled 810 miles with the wind, then turned around and traveled 720 miles against the wind. The wind speed was a constant

Question 424862: Kate flew her plane for 6 hours at a constant speed. She traveled 810 miles with the wind, then turned around and traveled 720 miles against the wind. The wind speed was a constant 15 mph. Find the speed of the plane.
What I really want to know is, how do you solve a problem like this? I don't really understand can you help me for future problems such as the one above?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
plane speed x mph
wind speed 20 mph

Distance with tail wind 810 miles
Distance against wind 720 miles
speed with wind x+20
speed against wind=x-20
Total flying time = 6 hours
Time with wind= 810/(x+20)
time against wind 720/(x-20)
Time with wind + time against wind =6
810/(x+20)+720/(x-20)=6
LCD =(x+20)*(x-20)
multiply the equation by the LCD
we get
810*(x-20)+720(x+20)=6(x^2-400)
810x-16200+720x+14400=6 X^2-2400
1530x-1800=6X^2 -2400
6X^2-1530x+1800-2400=0
6X^2-1530x-600=0
/6
X^2-255x-100=0
Find the roots of the equation by quadratic formula
a=1b=-255c=-100
b^2-4ac=65025-400
b^2-4ac=65425

x1=(255+255.78)/2
x1=255.39
x2=(255 -255.78 )/2
x2=-0.39
Ignore negative value
plane speed=255.39mph

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