<PRE><B>Question 1208853</B>
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Solution method #1....&lt;br&gt;
Let x be the number of degrees the hour hand moves during her workout.&lt;br&gt;
Draw a rough sketch showing the hands of the clock at both times on the same diagram to see that the number of degrees the minute hand moves is&lt;br&gt;
(360-(120-90)+x) = 330+x&lt;br&gt;
The minute hand moves 12 times as fast as the hour hand (the hour hand makes one revolution in 12 hours; the minute hand makes one revolution in 1 hour). So&lt;br&gt;
330+x = 12x
330 = 11x
x = 30&lt;br&gt;
The hour hand moves 30 degrees in 1 hour, so the duration of Tammy&#39;s exercises is 1 hour.&lt;br&gt;
ANSWER: Tammy exercises for 1 hour&lt;br&gt;
Solution method #2....&lt;br&gt;
The minute hand makes 12 revolutions in half a day; the hour hand makes one revolution.  Because of that, the times when the two hands make a particular angle are separated by intervals of 12/11 hours.&lt;br&gt;
When she starts her workout shortly after 6am, the minute hand is 90 degrees behind the hour hand.  The minute hand is also 90 degrees behind the hour hand at 3:00, so the time shortly after 6am when the minute hand is 90 degrees behind the hour hand is 3:00, plus 3 times 12/11 hours, which gives us a &quot;time&quot; of 6 3/11 hours.&lt;br&gt;
When she finishes her workout shortly after 7am, the minute hand is 120 degrees behind the hour hand.  The minute hand is also 120 degrees behind the hour hand at 4:00, so the time shortly after 7am when the minute hand is 120 degrees behind the hour hand is 4:00, plus 3 times 12/11 hours, which gives us a &quot;time&quot; of 7 3/11 hours.&lt;br&gt;
So the time between the beginning and end of her workout is exactly 1 hour.&lt;br&gt;
ANSWER: Tammy exercises for 1 hour&lt;br&gt;
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(Added later....)&lt;br&gt;
Having shown solutions by two different methods that I was familiar with in my initial response and finding the answer was 1 hour, I now see that there is a quite simple method for solving the problem.&lt;br&gt;
In any 1-hour interval, the angle between the hands changes by 30 degrees, because the hour hand moves 30 degrees while the minute hand moves a full 360 degrees.&lt;br&gt;
In this problem, since the angle between the hands changed by 30 degrees (from 90 to 120) during her workout, her workout must have been 1 hour.&lt;br&gt;
ANSWER (again) 1 hour&lt;br&gt;

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