Minneapolis-St. Paul International Airport is 8 miles southwest of downtown St. Paul and 10 miles southeast of downtown Minneapolis. To the nearest integer, how many miles apart are   downtown St. Paul and downtown Minneapolis?
Let downtown St. Paul, downtown Minneapolis, and the airport be located at $S$, $M$, and $A$, respectively. Then $\triangle MAS$ has a right angle at $A$, so by the Pythagorean Theorem, \[
MS= \sqrt{10^{2}+8^{2}}= \sqrt{164}\approx 12.8.
\] Therefore, the distance between the two downtowns to the nearest mile is  $\boxed{\text{13}}$ miles.