Answer
$\frac{v_{son}}{v_{mother}} = 2$
Work Step by Step
Let $m$ be the mass of the son.
Let $4m$ be the mass of the mother.
We can equate the kinetic energy of the son and the kinetic energy of the mother to find the ratio of their speeds.
$KE_{son} = KE_{mother}$
$\frac{1}{2}mv_{son}^2 = \frac{1}{2}(4m)v_{mother}^2$
$\frac{v_{son}^2}{v_{mother}^2} = 4$
$\frac{v_{son}}{v_{mother}} = 2$
