2007-01-09 21:29:59 · 8 answers · asked by TURAL H 1 in Science & Mathematics ➔ Mathematics
It's longer than 65 minutes (but not by much).
The hands are together at midnight, and the minute hand passes the hour hand just over 65 minutes later at 01:05 (and a bit).
This happens 11 times in a 12-hour period - so the exact answer is 65.4545...
Now stop watching the clock and do some work!
2007-01-09 21:38:28 · answer #1 · answered by Anonymous · 1⤊ 0⤋
Not 65 minutes, but exactly 65 minutes and 27.272727... seconds. Why?
Think of the clock with two hands: one as the minute hand (which travels around the clock every 1 hour) and the other the hour hand (which travels around the clock every 12 hours).
Now for a period of 12 hours, the minute hand has traveled 12 times around the clock, and the hour hand has traveled once around the clock.
Thus, for 12 hours the minute hand will overtake the hour hand 11 times.
Therefore, the minute hand will overtake the hour hand for every 12/11 hours, or
12/11 hours
= 1 1/11 hours
= 1 hour 5 minutes 27.272727... seconds
= 65 minutes and 27.272727... seconds
≈ 65 minutes
^_^
2007-01-09 21:54:47 · answer #2 · answered by kevin! 5 · 0⤊ 0⤋
Am I dumb, or what? The hour hand takes 12 hours to go all the way around the dial. The minute hand goes around in one hour. So how can it not overtake the hour hand every 65 minutes?
2007-01-09 21:37:30 · answer #3 · answered by Homeboy 5 · 0⤊ 0⤋
The minute hand moves 12 times as fast as the hour hand.
Let
x = speed hour hand
12x = speed minute hand.
r = number of revolutions of the hour hand
r + 1 = number of revolutions of the minute hand
t = time
This problem uses the formula
time = distance / rate
t = r/x = (r + 1)/(12x)
12xr = x(r + 1) = xr + x
11xr = x
r = 1/11
Since it is the hour hand this means that the amount of time that passed is:
(1/11)/(1/12) = 12/11 hours = 1 hour 5 minutes 27 3/11 seconds
The minute hand will overtake the hour hand every
65 minutes and 27 3/11 seconds.
2007-01-09 21:48:17 · answer #4 · answered by Northstar 7 · 1⤊ 0⤋
Luis is close but not quite right.
In the hour that it takes the minute hand to go around the hour hand has moved one number which is both one hour and 5 minutes.
Just imagine both hands at noon. When the minute hand gets back to 12 the hour hand has moved to 1. Thus it takes 5 more minutes for the minute hand to pass the hour hand.
2007-01-09 21:37:56 · answer #5 · answered by modulo_function 7 · 0⤊ 0⤋
The half the width of the sum of both hands is 5 minutes.
2007-01-09 21:34:13 · answer #6 · answered by Luis U 2 · 0⤊ 0⤋
Because in the hour it takes the minute hand to complete one revolution, the hour hand has moved forwards itself.
2007-01-09 21:35:54 · answer #7 · answered by Morgy 4 · 0⤊ 0⤋
the reason beeing your watch working exactly as it should be. It's good watch, what's the brand??
2007-01-09 22:26:18 · answer #8 · answered by riZi 3 · 0⤊ 0⤋