Since the distance between city A and B is 100 miles, and city B and C are 50 more miles apart than city A and B, then city B and C are 100+50 = <<100+50=150>>150 miles apart.
The plane's total flying distance between cities A and C is 100+150= <<100+150=250>>250 miles.
The distance between city C and city D is twice the distance between city B and city C, meaning city C and city D are 2*150 = <<300=300>>300 miles apart.
The plane flies a distance of 250+300 = <<250+300=550>>550 miles from city A to city D.
#### 550