SOLUTION: an airplane flying against the wind travels 500 miles in the same amount of time that it would take to travel 600 miles with the wind. if the speed of the wind is 50 miles per hour

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Question 117498: an airplane flying against the wind travels 500 miles in the same amount of time that it would take to travel 600 miles with the wind. if the speed of the wind is 50 miles per hour, what is the speed of the plane in still air
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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an airplane flying against the wind travels 500 miles in the same amount of time that it would take to travel 600 miles with the wind. if the speed of the wind is 50 miles per hour, what is the speed of the plane in still air
:
Learn this method and you can do most of these type problems:
:
Let s = speed of the plane in still air
then
(s-50) = speed against the wind
and
(s+50) = speed with the wind
:
It says the two trips take the same time, write a time equation:
Time = distance/speed
:
Against time = with time
500%2F%28%28s-50%29%29 = 600%2F%28%28s%2B50%29%29
:
Cross multiply
600(s-50) = 500(s+50)
:
600s - 30000 = 500s + 25000
:
600s - 500s = 25000 + 30000
:
100s = 55000
:
s = 55000%2F100
:
s = 550 mph in still air
:
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Check solution by finding if the times are, indeed, equal
Speed with the wind = 600 mph and speed against 500 mph
:
600/600 = 1 hr
500/500 = 1 hr