SOLUTION: a plane flies 2000 mile in 8 hours, with a tailwind all the way. The return trip on the same route, now with a headwind, takes 10 hours. Assume both remain constant, find the speed

Question 757743: a plane flies 2000 mile in 8 hours, with a tailwind all the way. The return trip on the same route, now with a headwind, takes 10 hours. Assume both remain constant, find the speed of the plane and the speed of the wind.
Answer by tasmart(9) (Show Source): You can put this solution on YOUR website!
tailwind speed of plain plus speed of wind p+w
headwind speed of plain minus speed of wind p-w
8 hours times p+w=2000
10 hours times p-w=2000
systems of equations with two variables.
8(p+w)=2000
10(p-w)=2000
distribute:
8p+8w=2000
10p-10w=2000

8p=2000-8w
p=250-w
now substitution:
10p-10w=2000
10(250-w)-10w=2000
2500-10w-10w=2000
-20w=2000-2500
-20w=-500
w=-500/-20
w=25 miles speed of wind.
8p+8(25)=2000
8p+200=2000
8p=2000-200
8p=1800
p=1800/8
p=225 speed of plain.
8(225)+8(25)=2000
200+1800=2000
10(225)-10(25)=2000
2250-250=2000
speed of wind is 25mph speed of plain is 225mph

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