In a seismic survey, a horizontal layer of velocity $v_1 = 3.0$ km/s overlies a half-space of velocity $v_2 = 5.0$ km/s. The crossover distance (where the direct arrival and the refracted head-wave arrival reach the geophone at the same time) is measured to be $x_{cross} = 20$ km. What is the depth $z$ of the horizontal boundary?