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Example Starting Time: 10:15 Ending Time:2:15 Elapsed Time: 4 hours. 11 o' clock, 12 o' clock, 1 o' clock, 2 o' clock. Total, 4 hours. So the answer to your question is yes...
At 3 hours 45 minutes there is not an acute angle between the hands of the clock (unless you extend the hands backwards).
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This problem can be solved as follows: The angle Ah of the hour hand of a clock, measured from the position at noon or midnight when the hour and minute hands exactly coincide, is Ah = (360 degrees/12 hours)th, where th is the time in hours, including fractions of hours, because the hour hand moves the entire 360 degrees around the clock in 12 hours. Similarly, the angle Am of the minute hand = (360 degrees/60 minutes)tm, where tm is the time in minutes only, including fractions of minutes. The stated time is 3 + 40/60 + 20/3600 hours = 3.672222... hours and the angle is therefore about 110. 11666666... degrees, using the formula above. The time in minutes only is 40 + 20/60 = 40.33333...., so that the angle of the minute hand is 242 degrees. The difference between them is therefore about 131.833..... degrees, or in fraction form 131 and 5/6.
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