The Bride of the First House (bride) wrote,
The Bride of the First House
bride

I like Math, I always have

I helped my brother with his Math homework tonight. He's in Grade 9.

An aircraft travels 5432 km from Montreal to Paris in 7 h and returns in 8 h. The wind speed is constant. Determine the wind speed and the speed in still air.

                                   ---> wind
Let x = speed in still air    M ---------------------> P
    y = wind speed               v = (x + y)
    d = 5432 km                  t = 7h
     d                             ---> wind
v = --- , d = vt              M <--------------------- P
     t                           v = (x - y) km/h
                                 t = 8h
Since the distance from A to B is the same as the distance from
B to A, we have:
    7x + 7y = 5432
    8x - 8y = 5432
Add the two lines to get:
    15x - y = 10864
        15x = 10864 + y
Subtract the two lines to get:
   -x + 15y = 0
          x = 15y
Plug in '15y' for 'x':
       225y = 10864 + y
       224y = 10864
          y = 48.5
Plug in 'y':
          x = 15(48.5)
          x = 727.5
Wind speed: 48.5 km/h
Speed of aircraft in still air: 727.5 km/h

Q.E.D.
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