Question 1128343: Hi!
I've been working on this problem for awhile and can't figure out how to set it up. The problem says:
At what time between 3 and 4 o'clock do the hands of a clock coincide?
Thank you!
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The minute hand goes around 60 times for the hour hand to go 1/12 of the way.
One way to look at it is by degrees.
At 1 pm, the minute hand is vertical, and the hour hand has gone 30 degrees around (1 pm spot)
The minute hand moves 6 degrees a minute
The hour hand is 30 degrees ahead and is moving 30 degrees/60 minutes or 1/2 degree minute
The minute hand has to catch up 30 degrees and is catching up at 6-1/2, or 5.5 degrees per minute
30/5.5=5.4545 minutes to catch up.
this is 60*5.4545 or 327.27 sec or 5m27s
This will be the same for each hour. At 2 pm, they will coincide at 10m54s, and at 3 pm 15.81.818 or 15.81.82
minutes, which is 16m22s
They will coincide at 3:16.22
11 times the hands are together going around the clock
60/11=5.4545, and that is the time (+1 hour) in between the times the hands coincide.
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