Your idea matters-14

For this race, Nonte & Fonte both:

1) Begin from rest ( $v_{0}=0$ ),

2) Travel a distance of $120$ meters,

3) Have uniform accelerations.

Because of #3 above, we require the kinematic equations $d = v_{0}t + \frac{1}{2}at^2, v^2 = v^{2}_{0} + 2ad$ . If we susbstitute the first expression into the second one, we obtain the expression for the final velocity: $v^2 = 2d(\frac{2d}{t^2}) = \frac{4d^2}{t^2}.$

The ratio of Nonte and Fonte's kinetic energies can be computed according to:

$\frac{KE_{N}}{KE_{F}} = \frac{(1/2)m_{N}v^{2}_{N}}{(1/2)m_{F}v^{2}_{F}} = \frac{m_{N}(4d^2 / t^{2}_{N})}{m_{F}(4d^2 / t^{2}_{F})} = \frac{m_{N}t^{2}_{F}}{m_{F}t^{2}_{N}} = \frac{(60)(15^2)}{(70)(12^2)} \approx 1.339 : 1$

or $\boxed{x = 1.339}.$