Qian used the rule “divide the length of a piece of wood by 3 to get the number of nails needed.” If 3 nails are needed for a piece of wood that is 9 inches and 13 nails are needed for a piece of wood that is 39 inches, what is the length of a piece of wood that requires 8 nails?
Using the given information, we can set up a ratio:
$\frac{9}{3} = \frac{39}{13}$
To find the length of a piece of wood that requires 8 nails, we can set up another ratio: $\frac{x}{8} = \frac{39}{13}$
Cross-multiplying to solve for $x$, we get $13x = 312$, which gives $x = \boxed{24}$ inches.