The usual formula is d=v²/(2µg) where µ is the coefficient of friction of the road surface. We have to assume a value of µ, so let’s take 0.5. The formula then becomes d=v²/32 for g=32ft/s². So v²=32×175=5600 and v=74.8fps=51mph. For µ=0.4, v=66.9fps=45.6 mph, and for µ=0.6, v=82.0fps=55.9mph. When µ is small the skid is longer for the same speed. If µ=1, v=105.8fps=72.2mph, the maximum speed for maximum friction when the skid length is 175 feet. (When there is no friction, µ=0. This is more or less icy conditions and the skid length is effectively infinite.)
The kinetic energy of the vehicle is mv²/2. This energy is dissipated through the work done by friction. The normal force on a flat surface is mg. The frictional force is µmg and the work done is the frictional force acting over the distance d, the skid length. This work is µmgd=mv²/2, and d=v²/(2µg).