SOLUTION: A plane flies 300 miles with a tail wind in 1 hour. It takes the same plane 2 hours to fly the 300 miles when flying against the wind. What is the plane's speed in still air?
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Question 155931: A plane flies 300 miles with a tail wind in 1 hour. It takes the same plane 2 hours to fly the 300 miles when flying against the wind. What is the plane's speed in still air? Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=rate(speed) of plane in still air
Let r1=rate (speed) of tailwind
With tailwind: 300=(r+r1)*1
300=r+r1-------------------------------eq1
Against tailwind: 300=(r-r1)*2
300=2r-2r1------------------------------eq2
multiply eq1 by 2 and then add it to eq2:
600=2r+2r1----------eq1a
300=2r-2r1-------------eq2
900=4r divide each side by 4
r=225 mph---------------------------speed of plane in still air
substitute r=225 mph into eq1
300=225+r1 subtract 225 from each side
300-225=225-225+r1 collect like terms
75=r1 or
r1=75 mph----------------------speed of wind
CK
300=(225+75)*1
300=300
and
300=(225-75)*2
300=150*2
300=300
Hope this helps--ptaylor
