AMC 8 2009 Problem 21

Andy and Bethany have a rectangular array of numbers with $40$ rows and $75$ columns. Andy adds the numbers in each row. The average of his $40$ sums is $A$. Bethany adds the numbers in each column. The average of her $75$ sums is $B$. What is the value of $\frac{A}{B}$? $\textbf{(A)}\ \frac{64}{225} \textbf{(B)}\ \frac{8}{15} \textbf{(C)}\ 1 \textbf{(D)}\ \frac{15}{8} \textbf{(E)}\ \frac{225}{64}$