Time Traveling Ant

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It is 6 o'clock ..the ant from the tip of the clock's half foot Hour-hand must travel home to12 o'clock mark under the tip of 1ft Second-hand.

The clocks Minute hand is 9 inches.

The ant travels 1ft/min along the hands without stopping and reverses its direction when reaching the pivot end or the tip of the hands .

It can shift to any hand that is directly above or below it while resuming direction.

How long shall it take for the ant to arrive home?

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Posted (edited) · Report post

Wording made some of the rules sort of shaky.

3 minutes. Ant walks 6 inches to the base of the hour hand and switches to the second hand when it has the chance. He will have switched direction moving up the second hand, but can switch to the minute hand when the second hand overlaps it (approx 6 inches up it). He then walks up and back down the minute hand switching back onto the second hand as he is turning around to move back up the minute hand. After walking to the tip of the second hand he will have traveled 36 inches exactly meaning he is at the 12 and reached his home.

Edited by Nins_Leprechaun
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Posted · Report post

Wording made some of the rules sort of shaky.

Assuming the ant must travel on hands, I understand the ant has to:
a) wait for the Minute hand
b) switch to the Minute hand
c) walk to the end of the Minute hand

d) wait till the Minute hand reaches 12

which should happen at 7 o'clock.

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Posted (edited) · Report post

@ harey : yes all clocks hands are moving..but cant reach home via minute hand..

@nins: it must walk more than 6 in along hour hand ..to shift to the second hand..

Edited by TimeSpaceLightForce
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Posted (edited) · Report post

@ harey : yes all clocks hands are moving..but cant reach home via minute hand..

@nins: it must walk more than 6 in along hour hand ..to shift to the second hand..

I must be missing something then. If the clock starts at exactly 6 then in approx 30 seconds the second hand would overlap the hour hand. In that time the ant will travel 6 inches, the length of the hour hand. Yes there will be ever so slightly more than 30 seconds for this overlap to occur, but that fractional increase is irrelevant.

If you could clarify the problem with my reasoning here it would be appreciated.

Edit allow me to explain my interpretation of your description so you may correct any mistakes.

A clock has a 12 inch second hand, 9 inch minute hand and 6 inch hour hand.

The time is exactly 6 (hour hand at 6, second and minute hands at 12).

The ant is on the tip of the hour hand.

The ant must get to the tip of the second hand when it is pointed exactly at 12.

The ant moves 12 inches a minutes up and down a clocks hand, turning around when it reaches the tip or pivot of the hand it is on.

The ant may switch hands any time they overlap with no change to his current direction or speed of travel.

Edited by Nins_Leprechaun
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Posted · Report post

Wording made some of the rules sort of shaky.

3 minutes. Ant walks 6 inches to the base of the hour hand and switches to the second hand when it has the chance. He will have switched direction moving up the second hand, but can switch to the minute hand when the second hand overlaps it (approx 6 inches up it). He then walks up and back down the minute hand switching back onto the second hand as he is turning around to move back up the minute hand. After walking to the tip of the second hand he will have traveled 36 inches exactly meaning he is at the 12 and reached his home.

Yes 3 minutes is correct..ant walks on the hour hand for 30.0417secs,

then walks on the second hand for 30.9752 secs,

then walks on the minute hand 61.0169 secs,

then walks again on the second hand 57.9661secs..

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