Step 1: The rate of dehydration of alcohols follows the order of stability of the carbocation formed during the reaction.
Step 2: Tertiary alcohols (\( 3^\circ \)) form the most stable carbocation, followed by secondary alcohols (\( 2^\circ \)), primary alcohols (\( 1^\circ \)), and methanol (\( {CH}_3{OH} \)), which does not form a stable carbocation.
Step 3: Thus, the correct order is \( 3^\circ>2^\circ>1^\circ>{CH}_3{OH} \).