SOLUTION: A plane flies 600 miles against a steady 40 mph headwind, and then returns to the same point, with the wind. If the entire trip takes takes 8 hours, what is the plane�s speed in st

Question 565942: A plane flies 600 miles against a steady 40 mph headwind, and then returns to the same point, with the wind. If the entire trip takes takes 8 hours, what is the plane�s speed in still air?
Found 2 solutions by mananth, lwsshak3:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Plane speed x mph
wind speed 40 mph

against wind x- 40 mph
with wind x+ 40 mph

Distance= 600 miles

Time against + time with = 8 hours
t=d/r
600/(x+40)+600/(x-40)= 8

LCD = (x-40)(x+40)
600 *(x-40)+600(x+40)=8
600x-24000+600x+24000=8(x ^2-1600)
1200x= 8x ^2-12800
8x ^2-1200x-12800
8x^2+80x-1280x-12800=0
8x(x+10)-1280(x+10)=0
(x+10)(8x-1280)=0
8(x+10)(x-160)=0
x=160 which is positive
speed of plane = 160 mph

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A plane flies 600 miles against a steady 40 mph headwind, and then returns to the same point, with the wind. If the entire trip takes takes 8 hours, what is the plane�s speed in still air?
**
let x=speed of plane in still air
x+40=speed of plane with the wind
x-40=speed of plane against the wind
Travel time=distance/speed
..
600/(x+40)+600/(x-40)=8
divide by 8 to work with smaller numbers
75/(x+40)+75/(x-40)=1
LCD: (x+40)(x-40)
75(x-40)+75(x+40)=(x+40)(x-40)=x^2-40^2
75x-3000+75x+3000=x^2-1600
150x=x^2-1600
x^2-150x-1600=0
(x+10)(x-160)=0
x+10=0
x=-10 (reject, speed>0)
or
x-160=0
x=160 mph (speed of plane in still air)
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