1 knot = 0.868976 mph

let 't' is the time (in hours) of the flight from Chicago to Kansas City at speed of 440 knots. Then the distance between Chicago and Kansas is

t*440*0.868976 miles

it takes 3 hours longer from Kansas City to Chicago that is t+2 with a speed of 110 knots that is

(t+2)*110*0.868976 miles

now we can write

t*440*0.868976 = (t+2)*110*0.868976 divide both sides by 0.868976

440*t = 110*(t + 2)

t = 220/330

t = 2/3 hours

the distance is (2/3)*440*0.868976 = 254.9 miles approximately.