SOLUTION: Jim goes out on a walk just before 2 p.m. every day, when the hands of the clock make a 90 degree angle. He arrives back home after 3 p.m. when the hands of the clock first make a
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-> SOLUTION: Jim goes out on a walk just before 2 p.m. every day, when the hands of the clock make a 90 degree angle. He arrives back home after 3 p.m. when the hands of the clock first make a
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Question 1147940: Jim goes out on a walk just before 2 p.m. every day, when the hands of the clock make a 90 degree angle. He arrives back home after 3 p.m. when the hands of the clock first make a 20 degree angle. How many hours does he spend walking in June. Answer by greenestamps(13195) (Show Source):
The minute hand starts 90 degrees "behind" the hour hand and finishes 20 degrees "ahead of" the hour hand. So in the time the hour hand moves x degrees, the minute hand moves x+110 degrees.
But the minute hand moves 12 times as fast as the hour hand (12 revolutions in 12 hours for the minute hand; 1 for the hour hand.) So
The hour hand moves 10 degrees on each of his walks. Since the hour hand moves 30 degrees in 1 hour (360 degrees in 12 hours), each of his walks is 20 minutes, or 1/3 hour.
There are 30 days in June, so the number of hours he spends walking in June is 30*(1/3) = 10.
