SOLUTION: It takes an airplane 4 hours to travel 1000 miles with a tail wind. It takes the plane 5 hours to make the return trip against the wind? What is the speed of the plane and the wind

Algebraic solution:

Let a = speed of airplane in still air

    w = wind speed




(1)   (a+w)*4 = 1000  -->  4a + 4w = 1000

(2)   (a-w)*5 = 1000  -->  5a - 5w = 1000



Multiply the first equation by 5/4:  

      (1')  5a + 5w = 1250

      (2)   5a - 5w = 1000



Add (1') and (2):   10a = 2250  --> a = 225   (airplane speed 225mi/hr)



    Plug this value into (1):  4(225) + 4w = 1000 -->  4w = 100 --> w = 25

            (wind speed is 25mi/hr)

 

Let u be the speed of the plane at no wind, and let v be the speed of the wind.


The effective speed with the wind

    u + v = 1000/4 = 250 mph    (1)


The effective speed against the wind

    u - v = 1000/5 = 200 mph    (2)


Add equations (1) and (2)

    2u = 450

     u = 450/2 = 225 mph


Next, from equation (1)

     v = 250 - 225 = 25 mph.


ANSWER.   The speed of the plane at no wind is 225 mph.

          The speed of the wind is 25 mph.