2 comments to “The speed of a airplane in still air is 258 Km.the plane travels 832 Km against the wind and 1919 Km with the?”

1. zee_prime wrote:
   7. August 2007 at 2:23 pm :

   travelling against the wind its speed is 258-x so it takes 832/(258-x) hours. Travelling with the wind it takes 1919/(258+x) hours. Add these together and you get 19 hours. So (832(258+x) +1919(258-x))/(258^2-x^2)=19
   so (214656+832x+495102-1919x)/(66564-x^2)=19
   so709758-1087x=1264716-19x^2 so
   19x^2-1087x-554958=0. Check my working and solve this quadratic and x is the wind speed.

2. Bernie wrote:
   10. August 2007 at 10:41 am :

   First thing you need to do is get your units straight. Speed is Distance/Unit time, so 258 km is not a speed. 258 km/hour isa velocity
   Let’s assume you meant to say the plane speed is km/hr vs km as reported
   If the total time in the air is 19 hours, you can say that the plane spends X hours traveling “with the wind” and (19-x) hours “against the wind.
   Total distance traveled is 1919+832=2751 km
   Average speed is 2751/19= 145 km/hour- Note that the average speed is less than the zero wind speed of the airplane, so the airplane spends a lot of time going against the wind
   We assume the wind velocity is constant, so
   If we call the wind velocity Y, then the average velocity against the wind is (258-y)
   The average velocity with the wind is (258+y)

   So you can write an equation for distance=
   (258+y)*X + (258-y)*(19-x) = 2751 km traveled
   or you can also write an equation for the velocity for each leg
   (258-y)*x=832
   (258+y)*(19-x)=1919

   You also assume that Y has to be less than 258 (common sense)
   You can solve by iteration or creating a more elegant solution, if you round off to 1 or 2 significant figures you get
   y= 202 km/hour
   (time against the wind) is 14.82 hours
   time with the wind is 4.18 hours
   velocity against the wind is (258-202)=56 km/hour
   distance against the wind = 56*14.82= 830 km
   velocity with the wind= (258+202)=460 km/hr
   distance with the wind= 4.18*460= 1923 km
   Total distance traveled= 2753 km (close enough for an iterative solution)

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