SOLUTION: A plane traveled 312 miles to Baltimore and back. the trip there was with wind. It took 3 hours. The trip back was into the wind. The trip back took 6 hours. Find the speed of the

The average speed of the plane relative the earth was 312/3 = 104 miles per hour 
on the trip with the wind.


The average speed of the plane relative the earth was 312/6 = 54 miles per hour 
on the trip against the wind.


So, we can write these two equations

    r + w = 104   (1)    for the average speed of the plane with the wind,

    r - w =  54   (2)    for the average speed of the plane against the wind,


where "r" is the speed of the plane at no wind and "w" is the speed of the wind.


Add equations (1) and (2).  You will get then

    2r = 104 + 54 = 158,  r = 158/2 = 79.


Subtract equations (2) from equation (1).  You will get then

    2w = 104 - 54 = 50,  w = 50/2 = 25.


ANSWER.  The speed of the plane at no wind is 79 miles per hour.

         The speed of the wind is 25 miles per hour.