A commercial jet flies 1,500 miles with the wind. In the same amount of time it can fly 1,000 miles against the
wind. The speed of the jet in still air is 550 mph. Find the
speed of the wind.

As below

Step-by-step explanation:

we want to know  how long it took to fly  so make two equations and set them equal to each other using the variable t

so, use  d = r*t   where d= distance , r= rate ( speed) and t = time  

w= wind velocity (speed with direction)

1500=(w+550)*t

1000=(-w+550)*t

now make both equations with respect to t

1500/(w+550) = t

1000/(-w+550) = t

since they are both equal to t,  where t is the same amount of flying time, set the two equations equal to each other

1500/(w+550) = 1000/(-w+550)

now solve for w

1500w + 825,000 = -1000w+550,000

2500w= -275,000

w = - 110

the wind speed is 110 opposite of the planes direction but also, if the plane flies in the other direction with it.  

wind velocity (velocity is speed with a direction )   is 110 MPH

they are asking for speed, b/c we don't know anything about direction... that is which direction is the plane headed during it's flight therefore we also can't say anything about the   wind direction either.  :|

a is the correct