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In a clock, what is the distance traveled by the tip of the hour hand

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In a clock, what is the distance traveled by the tip of the hour hand  [#permalink]

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New post 05 Sep 2018, 22:37
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In a clock, what is the distance traveled by the tip of the hour hand in a 20-minute interval?

(1) The interval of 20 minutes takes place between 3:20 and 3:40.
(2) The hour hand has length 5.

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In a clock, what is the distance traveled by the tip of the hour hand  [#permalink]

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New post 06 Sep 2018, 00:00
We know that an hour will complete its round in 12 hours that is in 12*60=720mins.
Therefore our circle of 360 degree will be complete in 720 mins.
In 20 mins, the hour hand would have traveled 10 degrees

Our distance covered is (2*pi*r*10)/360 . {(2*pi*r*theta)/360 }

Statement 1
The interval of 20 minutes taken place between 3:20 and 3:40 is irrelevant since it mentions nothing a radius of the hour hand or any information about the circle.

In statemnet 2
The radius is given 5

Hence applying , (2*pi*5*10)/360
=5/18 *pi

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In a clock, what is the distance traveled by the tip of the hour hand  [#permalink]

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New post 06 Sep 2018, 00:07
Bunuel wrote:
In a clock, what is the distance traveled by the tip of the hour hand in a 20-minute interval?

(1) The interval of 20 minutes takes place between 3:20 and 3:40.
(2) The hour hand has length 5.


the distance traveled by tip is equal to the arc of the circle made by the tip..
this arc is dependent on the radius of the cicle made by the tip and angle covered by the hour hand in 20-minutes.

The hour hand travels 360 in 12 hr or in \(12*60=720\) minute, so \(\frac{360}{720 *20}=10\) in 20 minutes..
angle traveled = 10 degree...
so ARC=distance = \(area*\frac{10}{360} = \frac{\pi*r^2}{36}\)

Requirement - radius??

(1) The interval of 20 minutes takes place between 3:20 and 3:40.
Irrespective of the time, the distance will be the same
insuff

(2) The hour hand has length 5
so radius =5
suff

B
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In a clock, what is the distance traveled by the tip of the hour hand   [#permalink] 06 Sep 2018, 00:07
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