speed of a plane again

Question

Against the wind a commercial airline in South America flew
510
miles in
3
hours. With a tailwind the return trip took
2.5
hours. What was the speed of the plane in still? air? What was the speed of the? wind?

Answer 1

 

Let W = speed of the wind

 

Let P = Speed of plane

 

Rate * Time = distance

 

AGAINST THE WIND:

 

   Lets determine the planes rate, against the wind

 

   rate * time = distance

   rate * 3 = 510

   rate = 510/3 = 170

 

    Equation 1:  P - W = 170   ... (the head wind speed decreases the traveling speed)

 

WITH THE WIND:

 

   Lets determine the planes rate, with the wind

 

   rate * time = distance

   rate * 2.5 = 510 

   rate = 510/2.5 = 204

 

   Equation 2:  P + W = 204  ... (the tailwind increases the traveling speed)

 

So we have a system of equations involving the plane speed and the wind speed.  Solve for P using elimination method ... add the 2 equations and eliminate W.

 

   P  - W = 170

   P + W = 204

  --------------------

 2P         = 374

   P = 187

 

The planes speed is 187 miles per hour

 

 

Since P + W = 204   ... we can substitute 187 for P and solve for W

 

       187 + W = 204

        W = 204 - 187

        W = 17

 

The wind speed is 17 miles per hour