[Author Prev][Author Next][Thread Prev][Thread Next][Author Index][Thread Index]

*Subject*: Re: Tortured Algebra by an amateur*From*: Art Burke <aburke@VANSD.ORG>*Date*: Wed, 27 Feb 2002 15:45:57 -0800*Reply-to*: Assessment Reform Network Mailing List <ARN-L@LISTS.CUA.EDU>*Sender*: Assessment Reform Network Mailing List <ARN-L@LISTS.CUA.EDU>

>>> Allen.Flanigan@USPTO.GOV 02/27 2:09 PM >>>

...

Is there a more elegant solution using algebra?

-----------------------

Not exactly elegant, but kind of neat. I remember it because one of my older stepsons brought this problem home as a "brain-teaser" in his junior math class.

You get it by expressing the distance traveled by the hands aournd the clock as distance around a circle as a function of time (naturally enough.)

'Spose H is the hour hand M is the minute hand.

The hour hand goes around the clock once every 12 hours. So, its position around the circle

after t hours is

H(t) = ( 1/12 turn/hr x 360 deg/turn) x ( t hours),

or H(t) = 30t

The minute hand goes around the clock once every hour, so its position around the circle after t hrs is

M(t) = (1 turn/hr x 360 deg/turn) x (t hours)

or M(t) = 360t

By setting the distance formulas equal to each other, we can find the time when when the hands overlap.

H(t) = M(t)

30t = 360t

0 = 330t

t = 0

(Simplify things by requiring that time(0) equals 12 o'clock.)

Find the other solutions by realizing that for every hour the minute hand travels a multiple of 360 degrees farther than the hour hand.

M(t) = H(t) + 360N

360(t) = 30(t) + 360N

330t = 360N

t = (360 / 330) x N, which is

t = (12 / 11) x N

You can just plug in the values to find the times where the hands overlap.

I think I got something slightly wrong somewhere, but this is what I rememember. Oh, and I won't say whether it was me or my stepson who solved it, heheheh.

Art

--------------------------------------------------------------------------

To unsubscribe from the ARN-L list, send command SIGNOFF ARN-L

to LISTSERV@LISTS.CUA.EDU.

- Prev by Author:
**Re: sorry** - Next by Author:
**Re: EDUCATION AGENCY POSTS CHARTER SCHOOL REFORM RULES** - Previous by thread:
**Re: Tortured Algebra by an amateur** - Next by thread:
**Re: Tortured Algebra by an amateur** - Index(es):