Yahoo Answers: Answers and Comments for Complicated Math Problem For Solving (:? [Mathematics]
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From Anonymous
enUS
Thu, 20 Nov 2008 13:23:23 +0000
3
Yahoo Answers: Answers and Comments for Complicated Math Problem For Solving (:? [Mathematics]
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https://answers.yahoo.com/question/index?qid=20081120132323AA6WCgH
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From Brian D: the minute hand moves at 360 degrees per hour ...
https://answers.yahoo.com/question/index?qid=20081120132323AA6WCgH
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Thu, 20 Nov 2008 21:50:10 +0000
the minute hand moves at 360 degrees per hour ..6 degrees per minute
the hour hand at 30 degrees per hour , half a degree per minute
at the time she starts (after 4pm) the hour hand is at 120degrees, second hand at 0degrees
t*(6/min) = 120 + t(.5/min)
t(5.5/min)= 120 .......21.8181...[4hrs,21min, 49.08sec]
finish time is when hands form angle of 180
[t*6/min]  [120+[t*.5/min]] = 180
t* 5.5 = 300 ..
t= 54.545454 ...4hrs,54min32.4 sec
ends ....4:54:32
starts... 4:21:49
32:43

From Puzzling: Let's start at 4 pm. Here the minute hand...
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Thu, 20 Nov 2008 21:34:29 +0000
Let's start at 4 pm. Here the minute hand is straight up and the hour hand is on the 4. The angle between them is 120° (1/3 of 360°)
Now it takes 60 minutes for the minute hand to make a full revolution. So that is 360/60 = 6° per minute.
It take 12 hours (720 minutes) for the hour hand to make a full revolution. So that is 360/720 = ½° per minute.
In other words, each minute the angle between the two hands changes by a net of 5½°.
Let's first figure out how many minutes it will take from 4pm so that the hands are touching (i.e. 0° apart). That's 120° at a rate of 5½° per minute.
120 / 5.5 = 240/11 = 21 and 9/11 minutes
That's equal to 21 minutes 49 seconds
That's our starting time:
4:21:49
Now how many minutes to go another 180° (so the hands are opposite)?
180 / 5.5 = 360/11 = 32 and 8/11 minutes
That's equal to 32 minutes 44 seconds
Adding that to the time of 4:21:49 we get 4:54:33
Answers:
Part 0  She starts working at 4:21:49 when the hands are together.
Part 1  It takes 32 minutes 44 seconds for her to finish the problem.
Part 2  Her ending time is 4:54:33 pm when the hands are opposite each other.

From demaja: well, it takes her 30 min, because the hands w...
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Thu, 20 Nov 2008 21:36:55 +0000
well, it takes her 30 min, because the hands were together then exactly opposite, in order to do this, half an hour must have past. For the other part, if you think about the tic marks on a a clock, there are five marks between hours (after the four to the five.) So, each mark represents a 12 minute increment. Now, in order to for the hands to start out on top of eachother, she would have needed to start at least around 4: 20 (a little after actually). It can't be at the 36 minute tick mark, b/c then it's too late to complete the half hour, so the start is around 4:24 and the end 4:54 but you'll have to do the finer tuning yourself ^^

From R.N.: part 1 30 minutes
part 2 4:30 p.m.
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Thu, 20 Nov 2008 21:54:10 +0000
part 1 30 minutes
part 2 4:30 p.m.