document.write( "Question 1185859: How many minutes after five o’clock will the hands of the clock be perpendicular for the second time? \n" ); document.write( "

Algebra.Com's Answer #816728 by greenestamps(13198) $\"\"$ $\"About$

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\n" ); document.write( "I have seen students solve this kind of problem by many different methods similar to the one shown by the other tutor.

\n" ); document.write( "Here is the method I like....

\n" ); document.write( "The hour hand makes 1 revolution every 12 hours; the minute hand makes 12. Since both rotate at constant rates, any particular angle between the two hands will be formed 11 times every 12 hours. That means the interval between successive times that a particular angle is formed is 12/11 hours.

\n" ); document.write( "The second time after 5 o'clock that the hands form a 90 degree angle, the minute hand is 90 degrees ahead of the hour hand.

\n" ); document.write( "The minute hand is 90 degrees ahead of the hour hand at 9:00.

\n" ); document.write( "So the time between 5 and 6 o'clock when the minute hand will be 90 degrees ahead of the hour hand is 8 times 12/11 hours after 9:00, which is 8 times 1/11 hour after 5:00.

\n" ); document.write( "8*1/11 hours = 8/11 hours = 8/11(60 minutes) = 480/11 minutes = 43 7/11 minutes.

\n" ); document.write( "ANSWER: The second time after 5 o'clock that the two hands are perpendicular to each other is 43 7/11 minutes after 5 o'clock.

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