SOLUTION: Flying against a headwind, a plane covers 900 miles in 2 hours. The return trip with a tailwind only takes an hour and a half. Find the speed of the wind, and the speed of the plan

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Question 437577: Flying against a headwind, a plane covers 900 miles in 2 hours. The return trip with a tailwind only takes an hour and a half. Find the speed of the wind, and the speed of the plane within the air mass.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
against wind 2.00 hours
with wind 1.50 hours

Distance = same=900
plane speed =x
wind speed =y
t=d/r
900/(x-y)=2.00
2(x-y)= 900.00
2x-2y=900 ....................1
900/(x+y)=1.50
1.50(x+ y)=900
1.50x+1.50y=900 ...............2
Multiply (1) by 1.50
Multiply (2) by 2.00
we get
3x-3y=1350
3x+3y=1800
6x=3150
/6
x=525mph plane speed

plug value of x in (1)
2x-2y=900
1050-2y =900
-2y=900-1050
-2y=-150
y=75 mph wind speed