can you find the answer?

Question

Tell me soonest time to the nearest second the hour hand and minute hand align on a clock after noon.

Answer 1

The speed of the hour hand is 2pi/12 radians per hour

The speed of the minute hand is 2pi radians per hour.

The minute hand will cross the hour hand sometime in the second hour (by observation)

Let 2pi(h -1) = 2pi(h)/12

h(2pi - 2pi/12) = 2pi
h = 1/(1 - 12)
= 1.0909...
= 1 hour 5 minutes 27 seconds

Answer 2

first, lets clerify the definition of noon
I know of noon as 12:00:00
http://wwp.greenwichmeantime.com/info/noon.htm

depends on how the clock was made and wether it jumps clicks or is smooth

jumping = hands are aligned at 12:00:01pm - 12:00:59 pm
(they are STILL aligned at the second "AFTER" noon until the next minute)

clicking / smooth minute hands = hands will align at 1:05:27PM because even 1 second "AFTER" noon the smooth sweeping minute hand is no longer perfectly aligned to the hour hand
AND at 1:05 the hands won't meet because the hour hand moves just a little. so we need to give the minute hand a few seconds to move just a bit

total minute hand moves - 1 rev = angle hour hand moves
(1 rev/hour) × (t hours) - 1 rev = (1 rev/12 hours) × (t hours)
[(1 rev/hour)-(1 rev/12 hours)] × (t hours) = 1 revolution
(11/12 rev/hour) × (t hours) = 1 revolution
t = 12/11 hours

The hands of the clock are aligned every 12/11 hours which equals 1.090909 hours. To convert this number of hours into hours, minutes, and seconds, multiply 0.090909 hours by 60 to give 5.454545 minutes. Multiply 0.454545 minutes by 60 to give 27.2727 seconds.

1:05:27.2727272727272

Answer 3

Hi. The minute hand has to move at least one revolution. The hour hand moves one minute, or about 1/60th of an hour. So I would say 1/60th of an hour plus 1 second. 61 seconds.

Answer 4

1h 11m 0s.