Brain Teasers
A Time Teaser
Between two and three o'clock, someone looked at the clock and mistook the minute hand for the hour hand. Consequently the time appeared to be fifty-five minutes earlier than it actually was. What time was it?
Hint
There is a fraction involved in the precise answer, however this is not a mathematics test. If you get the answer within the nearest minute or so, consider your answer correct.Answer
The time must have been precisely 5 and 5/11 minutes past two o'clock. If you got 5 minutes or 5 and a half minutes after two, consider yourself correct.Hide Hint Show Hint Hide Answer Show Answer
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Comments
Since times shorter than 1 second are not usually given in 11th of a second: -----
the time is 25:27.27 plus, yes, 3/1100 second.
the time is 25:27.27 plus, yes, 3/1100 second.
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Sorry. Ignore that last one. I was in the wrong forum ...
ahem.
you must factor in the movement of the hour hand during the hour!
you must factor in the movement of the hour hand during the hour!
I believe the answer is incorrect. Firstly, the big hand must be before the little hand or else the time would be later rather than earlier when the hands are swapped. Thus let the time be x minutes past 2 (where x is less than 10). Now the big hand moves 6 degrees each minute while the hour hand moves 1/2 degree per minute. From the vertical the hour hand has moved 60 (2 O'clock) + x/2 degrees. The minute hand has moved 6x. The angle between them is 60 + x/2 - 6x.
Now 55 minutes earlier is (x+5) past one. The hour hand has moved 30(1 O'clock) + (x+5)/2 while the minute hand has moved 6(x+5).
The angle between them is 6(x+5) - (30 +(x+5)/2).
60 + x/2 - 6x = 6(x+5) - (30 + (x+5)/2)
60 - 11x/2 = 11x/2 - 5/2
62.5 = 11x or 125 = 22x
x = 5 15/22
The time is 25:40.9
(Comments?)
Now 55 minutes earlier is (x+5) past one. The hour hand has moved 30(1 O'clock) + (x+5)/2 while the minute hand has moved 6(x+5).
The angle between them is 6(x+5) - (30 +(x+5)/2).
60 + x/2 - 6x = 6(x+5) - (30 + (x+5)/2)
60 - 11x/2 = 11x/2 - 5/2
62.5 = 11x or 125 = 22x
x = 5 15/22
The time is 25:40.9
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