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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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      Log On


   

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(39616) About Me  (Show Source):
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                    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 3869%2F%28r-10%29-3869%2F%28r%2B10%29=20. Simplify and solve.

Answer by greenestamps(13198) About Me  (Show Source):
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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:

3869%2F%28x-10%29-3869%2F%28x%2B10%29=20

Multiply everything by the common denominator:

3869%28x%2B10%29-3869%28x-10%29=20%28x%2B10%29%28x-10%29
3869x%2B38690-3869x%2B38690=20%28x%5E2-100%29
77380=20x%5E2-2000
79380=20x%5E2
x%5E2=3969
x=63

ANSWER: The speed of the plane in still air is x = 63mph

Answer by ikleyn(52776) About Me  (Show Source):
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.

This airplane moves only slightly faster than a haymaker.



Answer by Alan3354(69443) About Me  (Show Source):
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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.