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?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52782)   (Show Source):
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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?
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We will measure angles starting from the position of the hour and the minute hands vertically up, at 12:00 (midday, the noon).
The minute hand makes one full rotation in one hour, so its angular velocity is 360 degrees per hour, or
360/60 = 6 degrees per minute.
The hour hand makes one full rotation in 12 hours, so its angular velocity is 360 degrees per 12 hours, or
360/12 = 30 degrees per hour = 30/60 = 0.5 degrees per minute.
At 6:00 pm, the hour hand is in position 6*30 = 180 degrees from vertical position clockwise.
The minute hand is in vertical position (= 0 degrees) at that time.
"t" minutes after 6:00 pm, the hour hand is in position 180 + 0.5t degrees from vertical up;
the minute hand is in position 6t degrees.
After 6:00 pm, the hour hand and the minute hand make the right angle for the first time, when 180 + 0.5t = 6t + 90 degrees.
From this equation, we find
180 - 90 = 6t - 0.5t, or 5.5t = 90, t =  = 16.3636... minutes.
After 6:00 pm, the hour hand and the minute hand make the right angle for the second time, when 6t = 180 + 0.5*t + 90 degrees.
From this equation, we find
6t - 0.5t = 180 + 90, or 5.5t = 270, t =  = 49.0909... minutes.
ANSWER. Ian was out with his dog 49.0909 - 16.3636 = 32.7272 minutes = 32 minutes and 44 seconds (approximately.
Solved.
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- Clock problems
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Answer by greenestamps(13200)  (Show Source):
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