Solution
Letx represent the airspeed of the plane, and let y represent the speed of the wind, both in kilometers per
hour. When the plane flies against the wind, the wind takes away from its groundspeed. Therefore
x− y= 750
Let’s put this equation into SI form. Subtracting x from each side gives us
−y=−x+ 750
Multiplying through by −1 tells us that
y= x− 750
When the plane flies with the wind, the wind adds to its groundspeed. That means
x+ y= 990
To morph this into SI form, we can subtract x from each side, getting
y=−x+ 990
Now let’s mix the right sides of these two SI equations:
x− 750 =−x+ 990
When we add 750 to each side, we obtain
x=−x+ 1,740
We can add x to each side to get
2 x= 1,740
Finally we divide through by 2, discovering that
x= 870
Now we know that the airspeed of the plane is 870 km/h. Let’s plug this value into one of the SI equations.
We can use the first one, getting
y =x− 750
= 870 − 750
= 120
This tells us that the wind is blowing at 120 km/h with respect to the earth.
254 Two-by-Two Linear Systems