SOLUTION: Nate flies a plane against a headwind for 3869 miles. The return trip with the wind took 20 hours less time. If the wind speed is 10 mph, how fast does Nate fly the plane when ther

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Question 1193696: Nate flies a plane against a headwind for 3869 miles. The return trip with the wind took 20 hours less time. If the wind speed is 10 mph, how fast does Nate fly the plane when there is no wind?
Found 4 solutions by josgarithmetic, greenestamps, ikleyn, Alan3354:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
                    SPEEDS      TIMES                 DISTANCE

AGAINST WIND         r-10       3869/(r-10)              3869

WITH WIND            r+10       3869/(r+10)              3869

DIFFERENCE                        20

With those, you can setup and continue with . Simplify and solve.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Let x be the plane speed (mph).

Then its speed with the wind is x+10, and its speed against the wind is x-10.

The time for flying 3869 miles with the wind is 3869/(x+10); the time for flying 3869 miles against the wind is 3869/(x-10).

The time for flying with the wind was 20 hours less than the time for flying against the wind:



Multiply everything by the common denominator:








ANSWER: The speed of the plane in still air is x = 63mph
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

This airplane moves only slightly faster than a haymaker.



Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Driving would be better than that.
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The people in the plane can look down and see vehicles on the roads passing them.
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