Let S be the speed of the plane in still air. With a headwind its speed is S-w where w is the headwind speed and S+w for the tailwind.
Distance is 270 miles. 270=3(S-w)=1.8(S+w)
3S-3w=1.8S+1.8w, 1.2S=4.8w, S=4w.
So 270=3(3w) and w=270/9=30mph. So S=120mph.
Wind speed is 30mph, plane speed is 120mph.