2006/07 AHSMC Part 1 Problem 4

In a city, all streets run north-south or east-west, dividing the city into squares. $A$, $B$, $C$ and $D$ are four students who live at four street intersections which define a rectangle, with $A$ and $C$ at opposite corners of this rectangle. They all go to the same school, which is at some street intersection within this rectangle. Each goes to school by a most direct route along streets. $A$ travels $10$ blocks, $B$ $20$ blocks and $C$ $50$ blocks. The number of blocks $D$ travels is