PR 4 # 21
 

Four cities, A, B, C, and D, lie at the vertices of a rectangle. Inside this imaginary rectangle there is a fifth city, E, which is exactly 33 miles from A and 56 miles from C. E also happens to be an integral number of miles from the other two cities, being further from B than from D. If the distance between B and C is three times that of E from D, how far, to the nearest half mile, is A from B?

[spoiler]58.5 miles[/spoiler]