Show me the steps and calculation to solve How far from the point of a hazard should the following warning signs be placed?

$($a$)$ A $$STOP ahead$$ warning sign on a road with a posted speed limit of $50$ mi$/$hr$.$

$($b$)$ A $$curve ahead$$ warning sign with an advisory speed of $30$ mi$/$hr on a road with a posted speed

limit of $45$ mi$/$hr$.$

$($c$)$ A $$merge ahead$$ warning sign on a ramp with an $85$th percentile speed of $35$ mi$/$hr$.$