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When the hour hand moves from 4 to 5 in an hour at what time do the minute hand and...

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christiano-cr7 | Salutatorian

Posted July 19, 2013 at 6:16 PM via web

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When the hour hand moves from 4 to 5 in an hour at what time do the minute hand and hour hand come together?

A)4:18 `(1)/(3)`

B)4:21 `(9)/(11)`

C)4:30

D)4:22

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 19, 2013 at 6:30 PM (Answer #1)

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The minute hand passes the hour hand between `4.20` and` 4.25` , say at `4` hours and` (20+t)` minutes .The speeds of the minute hand and the hour hand are `(2pi /60)`  =`( pi/30)` radians per minute and               `(2pi/12)` `/60` `=pi/360` radians per minute respectively .Now         `(20+t)( pi/30) =(2pi/3)+(20+t) (pi/360)`

`(20+t) ((1/10)-(1/120))=2`

`t=240/11-20=20/11`

So at `4:21(9/11)` , the minute hand passes the hour hand.

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