Question 1193697: A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour 12 minutes. What is his speed in still air, and how fast is the wind blowing?
Answer by greenestamps(13214)   (Show Source):
You can put this solution on YOUR website!
His speed flying against the wind is 180/2 = 90mph.
1 hour 12 minutes is 1 1/5 hours, or 6/5 hours. His speed flying with the wind is 180/(6/5) = 150 mph.
So
plane speed plus wind speed = 150mph
plane speed minus wind speed = 90mph
You can solve that algebraically if you want (or if you need to)...
p+w=150
p-w=90
solve using basic algebra
But this kind of problem can be solved using logical reasoning.
Adding the wind speed to the plane's speed gives 150mph; subtracting it from the plane's speed gives 90mph. That means the plane's speed is halfway between 90 and 150mph -- 120mph. And then the wind speed is the difference between 120mph and 150mph (or between 120mph and 90mph) -- 30mph.
ANSWERS:
plane speed: 120mph
wind speed: 30mph
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