When a plane flies with the wind, it travels 800 miles in 4 hours. Against the wind it takes 5 hours to cover the same distance. Find the rate of the plane in still air and the rate of the wind.


Hello Tim.

When the plane flies with the wind, you add the wind speed to the air speed to get the ground speed. Since it takes 4 hours to cover 800 miles along the ground, that is 800/4 = 200 mile per hour ground speed. When the plane flies against the same wind, you subtract the wind speed from the air speed to get the ground speed. In this case (5
hours to cover 800 miles), the ground speed is 800/5 = 160 miles per hour).

The air speed is the same for both trips and the wind speed is also the same. So you can think of it like this:

If I start with some air speed and add the wind speed, I get 200. If I start with the same air speed and subtract the wind speed, I get 160. So, what is the wind speed?

Hope this helps,
Stephen La Rocque>

Tim wrote back,

Thanks for the answer but I knew that. I guess what I was wanting to
know was how to write it in algebraic form, system, with the x's & y's.


Hi Tim.

If, on the other hand, you want to solve the problem algebraicly, then
you could try this approach:

Let a = the airspeed
Let w = the windspeed

a + w = 200
a - w = 160

Now you can add the two equations:
a + w + a - w = 200 + 160.

You'll find the value of a and with that you can find the value of w.
Stephen La Rocque.