ckowen wrote:i know the table you do where you set it up but im just utterly baffled as how to set this one up to find the speed of the plane in still air.
The "in still air" part is a fancy way of saying "what the speedometer reads" (or whatever they call it in a passenger plane). The speedometer reading and the actual speed are not necessarily the same thing. For instance, if your car is stuck on ice, your speedometer might be reading "60", while the car is actually slowly drifting backwards. Or think of trying to row a boat up
a waterfall: you can row like crazy, but you ain't goin' up!
So the secret
here is to account for the two input speeds with result in the one output speed: the speedometer reading for the plane, and the wind. On their trip out, the wind is against them, pushing them back, and thus subtracting from what the plane's engines are doing. On their trip back, the wind with with them, pushing them forward, and thus adding to what the plane's engines are doing.
Once you set up the "rate" part of your table with this information, use the fact that, whatever the distance was, it was the same in each direction. Set the "rt" expressions equal, and solve for the reading of the plane's speedometer.