SOLUTION: A PLANE FLIES FROM LOS ANGELES TO LAS VEGAS. THE TRIP IS 300 MILES. THE PLANE HAS 50 MPH TAILWIND (WITH THE PLANE). THE PLANE IMMEDIATELY FLIES BACK TO LOS ANGELES AND EXPERIENCES

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Question 949373: A PLANE FLIES FROM LOS ANGELES TO LAS VEGAS. THE TRIP IS 300 MILES. THE PLANE HAS 50 MPH TAILWIND (WITH THE PLANE). THE PLANE IMMEDIATELY FLIES BACK TO LOS ANGELES AND EXPERIENCES A 100 MPH HEADWIND (INTO THE PLANE). IF THE ROUND TRIP TAKE 16 HOURS. HOW FAST WOULD THE PLANE FLY IN STILL AIR?
Answer by lwsshak3(11628) About Me  (Show Source):
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A PLANE FLIES FROM LOS ANGELES TO LAS VEGAS. THE TRIP IS 300 MILES. THE PLANE HAS 50 MPH TAILWIND (WITH THE PLANE). THE PLANE IMMEDIATELY FLIES BACK TO LOS ANGELES AND EXPERIENCES A 100 MPH HEADWIND (INTO THE PLANE). IF THE ROUND TRIP TAKE 16 HOURS. HOW FAST WOULD THE PLANE FLY IN STILL AIR?
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let x=speed of plane in still air
(x+50)=speed of plane with tailwind
(x-100)=speed of plane with headwind
travel time=distance/speed
..
300%2F%28x%2B50%29%2B300%2F%28x-100%29=16
lcd:(x+50)(x-100)
300(x-100)+300(x+50)=16(x+50)(x-100)
300x-30000+300x+15000=16(x^2-50x-5000)
600x-15000=16x^2-800x-80000
16x^2-1400x-65000
solve for x by quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=16, b=-1400, c=-65000
x≈121
HOW FAST WOULD THE PLANE FLY IN STILL AIR? 121 mph