2009 AMC 10A Problem 16

Let a, b, c, and d be real numbers with |a-b|=2, |b-c|=3, and |c-d|=4. What is the sum of all possible values of |a-d|?

\mathrm{(A)}\ 9 \qquad \mathrm{(B)}\ 12 \qquad \mathrm{(C)}\ 15 \qquad \mathrm{(D)}\ 18 \qquad \mathrm{(E)}\ 24

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.