document.write( "Question 1198138: Between 6 p.m. and 7 p.m. the hands of a clock make a ninety-degree angle on two occasions. If Jenny always leaves home to walk her dog when the first ninety-degree angle is formed, and arrives home when the second is formed, how much time, in hours, does Jenny spend walking her dog every week? \n" ); document.write( "

Algebra.Com's Answer #831671 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The time of day is not a necessary piece of information for solving the problem; the fact that the angles are 90 degrees at the beginning and end of each walk is sufficient.

\n" ); document.write( "Let t be the number of minutes that she spends walking her dog.

\n" ); document.write( "The hour hand moves 360 degrees in 12 hours, or 30 degrees per hour, or 0.5 degrees per minute; the minute hand moves 360 degrees in 1 hour, or 6 degrees per minute. So in t minutes the minute hand moves 6t degrees and the hour hand moves 0.5t degrees.

\n" ); document.write( "In the time that she is walking her dog, the minute hand goes from 90 degrees \"behind\" the hour hand to 90 degrees \"ahead of\" the hour hand, so the number of degrees the minute hand moves is 180 more than the number of degrees the hour hand moves:

\n" ); document.write( " $\"6t=0.5t%2B180\"$
\n" ); document.write( " $\"5.5t=180\"$
\n" ); document.write( " $\"t=180%2F5.5\"$ = 32.73 minutes to the nearest hundredth

\n" ); document.write( "ANSWER: approximately 32.73 minutes per day; 229.09 minutes per 7-day week

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