Math Is Fun Forum

jimbob

Member

Registered: 2009-07-23

Posts: 2

Difficulty with Time problem

Sorry this litle time problem is irritating me, anyone solve it?
At 6 o'clock the angle between the minute hand and hour hand on a clock is 180 degrees.
What precise time does this happen next?
I'm somwhere around 5 minutes and 28 seconds past 7, but not exactly 180 dgrees.
Anyone?

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Difficulty with Time problem

it starts off with hour hand at 180 degrees from 12 oclock , and minute hand at 0 degrees

at time t (in minutes), you have that the hour hand makes the angle

180+t/2 (in one hour (60min) it turns 30degrees)

and the minute hand

t*6   (in one hour (60min) ut turns 360degrees)

so

t*6 - (180+t/2) = 180

5.5t - 180 = 180
5.5t = 360
t = 65.454545454545... = 1hr 5min 27sec 273ms    and so on, to nearest second we have that the next time will be

07:05:27

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soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Difficulty with Time problem

At 6:00 the angle between the minute hand and hour hand on a clock is 180°.
At what precise time does this happen next?

              * * *
          *     |     *
        *       |       *
       *        |        *
                |
      *         |         *
      *         *         *
      *        /          *
              /
       *     /           *
        *               *
          *           *
              * * *

. .

. .

.

jimbob

Member

Registered: 2009-07-23

Posts: 2

Re: Difficulty with Time problem

Thanks both replies.
I followed same process, using sample times close to 07.05.
Came up with a similar function.
And my answer to be 1and 1/11th of an hour after the start time of 06.00.

Concluding (once I knew this value of course) that it changes 11 times within a 12 hour period.
So simply 1/11th of an hour is the key answer.

Phew!

Tigeree

Member

Registered: 2005-11-19

Posts: 13,883

Re: Difficulty with Time problem

Welcome to the forum, jimbob. And you're welcome for help any time you need it. Hmm.... your username seems to be of two others, jimmyR and bobbym. I was wondering when you would come...

Last edited by Tigeree (2009-07-24 14:04:02)

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