SOLUTION: In moving through 124 degrees, the minute hand of a clock sweeps out 9 times the area swept out by the hour hand when it moves 31 degrees. How many times is the minute hand longer

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Question 1117404: In moving through 124 degrees, the minute hand of a clock sweeps out 9 times the area swept out by the hour hand when it moves 31 degrees. How many times is the minute hand longer than the hour hand?
Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
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Without going into extended theorizing, you can write this proportion for areas


    %28124%2Ar%5E2%29%2F%2831%2AR%5E2%29 = 9,


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


Then from this proportion  r%5E2%2FR%5E2 = %289%2A31%29%2F124 = 9%2F4, and r%2FR = sqrt%289%2F4%29 = 3%2F2.


Thus  the minute hand is  3%2F2%29 times as long as the hour hand.

Answered and solved.