Math Is Fun Forum

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Puzzle based on actual situation encountered in real life

Zhylliolom asked me in another thread what I did for a living. Well, two years ago, I did some part-time work delivering newspapers in my local area. I had to bring the papers in a trolley round to houses and deliver them each week. Below is a typical route in each delivery round of mine:

AB is the pavement on which I wheel my trolley of papers; M and N are the doorsteps of two houses I have to deliver papers to. I am not allowed to wheel my trolley right up to the doorsteps. I have to leave my trolley on the pavement, walk up to each doorstep, deliver the paper, walk back to my trolley on the pavement, and resume my journey.

At first, I did the obvious route , namely AMACBNB. Soon I realized that I could actually walk across from one doorstep directly to the next (most of the houses were not separated by fences) – so I tried another route: ACMNCB (where C is the midpoint of AB).

The problem is: which route is shorter? AMACBNB, or ACMNCB?

You might also be interested in proving that if C is allowed to vary along the line AB, the distance MCN would be shortest if and only if C is the midpoint of AB.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Puzzle based on actual situation encountered in real life

Why can't you simply go AMNB if you can walk from door to door?

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Puzzle based on actual situation encountered in real life

I understand the problem. You get something similar when you park the car and need to visit two places ... do you park near the first, then go back to the car, drive to the second place ... or do you park partway between, walk to the first, then second, then back.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Puzzle based on actual situation encountered in real life

Thank you, MathsIsFun.

Maybe for the sake of this puzzle I should have pretended I was driving a car instead of moving a trolley. It would have been more obvious that you couldn’t drive your car into someone’s garden than it was that you couldn’t wheel your trolley in the same way.

Last edited by JaneFairfax (2007-05-08 04:49:59)

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Puzzle based on actual situation encountered in real life

Sorry for the misunderstanding! I suggested AMNB because I forgot that by the time you got to B the car would still be back at A!

pranshu

Member

Registered: 2006-02-21

Posts: 3

Re: Puzzle based on actual situation encountered in real life

I think if AM or BN >/= AB or MN then AMACBNB is shorter and vis a versa because AMACBNB IS 4*HEIGHT+2*BASE AND ACMNCB IS 4*BASE + 2*DIAGONAL in given fig.