An airplane can fly downwind a distance of 600 miles in 2 hours. The return
trip against the same wind takes 3 hours. Find the speed of the wind.

Let w = the speed of the wind
Let a = what the speed of the airplane would be if there were no wind

Then going, flying with the wind, the wind makes the plane go faster,
so we add the speed of the wind to what the speed of the plane would be
if there were no wind.  Therefore,

The actual speed going with the wind = a + w

Now we use DISTANCE GOING = SPEED GOING × TIME GOING
                      600 =  (a + w)×2
                      600 = 2(a + w)
Divide both sides by 2
                      300 = a + w

Now returning, flying against the wind, the wind makes the plane go 
slower, so we subtract the speed of the wind from what the speed of the 
plane would be if there were no wind.  Therefore,

The actual speed returning against the wind = a - w

Now we use DISTANCE RETURNING = SPEED RETURNING × TIME RETURNING
                      600 =  (a - w)×3
                      600 = 3(a - w)
Divide both sides by 3
                      200 = a - w 

Now you have two equations in two unknowns:

                      300 = a + w
                      200 = a - w 

Or maybe you would want to write them with the unknowns on the left:

                      a + w = 300
                      a - w = 200

Solve them and get a = 250 mph and w = 50 mph


So the speed of the airplane if there were no wind = 250 mph
and the answer to the problem is:

The speed of the wind is 50 mph

Edwin