First overtone of a closed pipe (3rd harmonic) is $f_c = 3v/(4L_c)$. First overtone of an open pipe (2nd harmonic) is $f_o = 2v/(2L_o) = v/L_o$. Given $f_c = f_o$, so $3v/(4L_c) = v/L_o$. This gives $L_c/L_o = 3/4$.