Problem 582

(20 points) In a rectangular parallelepiped $A B C D A_{1} B_{1} C_{1} D_{1}$, the lengths of the edges are known: $A B=60, A D=30, A A_{1}=15$. The midpoint of edge $A_{1} B_{1}$ is marked as point $E$, and the midpoint of edge $B_{1} C_{1}$ is marked as point $F$. Find the distance between the lines $A E$ and $B F$.