vehicle_energy_stored = 0.5 * mass* (speed^2)
energy_dissipated_in_skid = brake_force * distance
Set these two equations equal to each other, then solve for speed:
speed = sqrt( 2 * force * distance / mass )
In a 1.0 g panic stop (seldom reached by most passenger cars, unless they have high performance sticky tires, or unless the car is a Caprice 9C1...), the brake_force will very nearly be equal to the weight (mass*gravity) of the car, so
brake_force = mass * gravity
[Aside: if the braking can't reach 1 g, then the brake_force will be some factor less than mass * gravity; e.g. brake_force = 0.9*mass*gravity for a 0.9 g panic stop). Gravity is a constant based on how much the earth pulls on you: 32.2 ft/(sec^2) or 9.81 meters/(sec^2)
So the speed equation reduces to:
speed = sqrt( 2 * gravity * distance )
g = 9.81 meters/(sec^2)
and in your example, distance is 121 feet (36.9 meters), so
speed = sqrt ( 2 * 9.81 * 36.9 ) = 26.9 m/s or 60.1 mph
There are many little items not shown in the above: the energy stored in the rotating mass (wheels, tires), the number of wheels involved in the stop, and the change of front-to-rear wheel loading due to the decceleration acting on the center-of-mass of the car. The devil in those details aren't worth posting here.
H50's post has similar math, I'm just showing where it comes from.
HTH. - Ken