Question 1117404
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Without going into extended theorizing, you can write this proportion for areas


    {{{(124*r^2)/(31*R^2)}}} = 9,


where  r and R are the lengths of the minute and hour hands, respectively.


Then from this proportion  {{{r^2/R^2}}} = {{{(9*31)/124}}} = {{{9/4}}}, and {{{r/R}}} = {{{sqrt(9/4)}}} = {{{3/2}}}.


Thus  the minute hand is  {{{3/2)}}} times as long as the hour hand.
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Answered and solved.