Question 1173896: The rate of a small aircraft in calm air is 125 mph. If the wind is currently blowing south at a rate of 5 mph, how far north can a pilot fly the plane and return it within 4 h?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe the problem is stating that it takes 4 hours for the plane to return to where it started from.
if the plane is flying against the wind (going north), then the combined rate of the plane is 125 - 5 miler per hour = 120 miles per hour.
if the plane is flying with the wind (going south), then the combined rate of the plane is 125 + 5 = 130 miles per hour.
rate * time = distance.
on the return flight, the plane is flying at 130 miles per hour for 4 hours.
that's a distance of 4 * 130 = 520 miles.
that would be the distance that the plane could fly north before having to turn around so it could be back in 4 hours.
when traveling north, the combined rate of the plane and the wind is 120 miles per hour.
if it is to travel north for 520 miles, then it would take the plane 520 / 120 = 4 and 1/3 hours to travel north, while taking 4 hours to fly back.
that is one interpretation of this problem.
another interpretation assumes that the total time north and south is 4 hours total for the trip north and the trip south.
with this interpretation, the distance going north and south are the same.
i solve this to determine that the time to go north was 2.08 hours and the time to south was 1.92 hours.
the distance going north and going south was the same at 249.6 miles going each way for a total of 299.2 miles.
i'm not exactly sure which you are asking, but i provided you with answer assuming both assumptions.
pick the one you think is the correct interpretation.
let me know if you have any questions or if both of my interpretations are incorrect.
if they are, plese clarify in more detail what you are looking for.
if my second interpretation is the correct one and you need more details as to how i arrived at that answer, please let me know and i'll provide you with the detailed analysis of that.
theo
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