Algebra Know-It-ALL

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