For a given initial velocity, how does the time td it takes to stop on dry snow differ from the time tw it takes to stop on wet snow

let the friction coefficient on dry ice and wet ice is different and given as

= on dry ice

= on wet ice

now by friction force formula we can say

so the deceleration due to friction force is given as

now the deceleration due to friction force on both surface is given as

now the time to stop the two blocks can be calculated by kinematics

also for other block on wet ice we can say similarly

now the ratio of two time on two surfaces is given as

so this is the ratio of time on two surfaces