Brain Teasers
Clock Watcher
Some time after 2 O' Clock, the angle made between the minute hand and the vertical (12) on a clock is double the angle made between the hour hand and the vertical (12). What time is it?
Hint
What is the rate of travel of each hand on a clock?Answer
2:24 The hour hand makes an angle of 72 degrees while the minute hand makes an angle of 144 degrees.At exactly 2:00, the angle made by the hour hand is 60 degrees from vertical. If you let x = the number of minutes past 2:00 that we are looking for, then the hour hand will be at:
60 degrees + x / 60 min* 30 degrees
where x/60 min is the fraction of a full hour that has past, and is therefore the fractional distance that the hour hand has moved closer to the 3. The 30 degrees is the total angle between the 2 and the 3.
The final position of the minute hand will be:
x/30 min * 180 degrees
for the same reasoning as with the hour hand.
Since the minute hand will make twice the angle with vertical, you can set up the equation:
2*(60 + x / 60 * 30) = x / 30 * 180
Solving for x will give you 24 minutes. The time will be 2:24.
Hide Hint Show Hint Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments
This took a lot of work for me. Mostly because I was looking for the case where the angle with the minute is half the angle with the hour. Once I understood the problem correctly, I got the answer quickly. Thanks for the challenge!
Your explanation makes it harder than it is.
The minute hand moves 12 times faster than the hour hand and has to get to twice the angle as the minute hand. In terms of where the hour hand will be, this is the same as if the minute hand only moves 6 times faster than the hour hand and the minute hand just has to catch it. So the hour hand will be pointing at the 6/(6-1) * 10 = 12 minute mark and the minute hand will be pointing at the 2*12 = 24 minute mark.
Something like 8 seconds in my head.
The minute hand moves 12 times faster than the hour hand and has to get to twice the angle as the minute hand. In terms of where the hour hand will be, this is the same as if the minute hand only moves 6 times faster than the hour hand and the minute hand just has to catch it. So the hour hand will be pointing at the 6/(6-1) * 10 = 12 minute mark and the minute hand will be pointing at the 2*12 = 24 minute mark.
Something like 8 seconds in my head.
"and has to get to twice the angle as the HOUR hand..."
Need to slow down and proof read my comments.
Need to slow down and proof read my comments.
To post a comment, please create an account and sign in.
Follow Braingle!