Escalator Puzzle

10/2/08, 6:02 AM #1

Alex Yeilding
Guest

Escalator Puzzle

Frank and Sam are walking through an airport and come to an escalator. Both decide to climb as they ride the escalator, but Frank is more energetic, climbing two steps for every one taken by Sam. Frank reaches the top after taking 36 steps, while Sam gets there after taking 27 steps.

How long is the escalator?

Re: Escalator Puzzle

10/2/08, 12:19 PM #2

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Re: Escalator Puzzle

I think I know, but will wait to see if anyone else weighs in. Good problem. You might want to post these on Fridays so that we can have something every day.

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: Escalator Puzzle

10/2/08, 12:41 PM #3

Charles Yawn
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188 posts

Registered: 4/18/07

Duh... one floor?

Re: Escalator Puzzle

10/2/08, 2:07 PM #4

Alex Yeilding
Guest

Re: Escalator Puzzle

Friday. Will do.

You were quick with the solve! I really struggled with this one. No math beyond HS sophomore algebra, but I thought it was the hardest such problem I had seen.

There is also a solution involving very simple math, but I never saw it. I just slogged through all the variable substitutions.

Re: Escalator Puzzle

10/2/08, 2:10 PM #5

Alex Yeilding
Guest

That's _A_ right answer

Re: Escalator Puzzle

10/2/08, 2:22 PM #6

Bill Earl
Member
Offline
948 posts

Registered: 6/17/05

Re: Escalator Puzzle

Frank: 36+x=L

Sam: 18+x+9+x/2=L

Solving for x:

36+x=27+3x/2

or:

9=x/2

x=18

L=54

Re: Escalator Puzzle

10/2/08, 2:41 PM #7

Alex Yeilding
Guest

Re: Escalator Puzzle

You and Dan are too quick. I slogged through this with variables for rates for escalator, Sam, and Frank, and times for Sam and Frank, with tons of variable substitutions! :-(

And I have to admit that if this were on a multiple choice test, I would have quickly chosen "E: Insufficient information for a solution" and moved on!

Re: Escalator Puzzle

10/2/08, 4:18 PM #8

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Great minds think alike ;-)

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: Escalator Puzzle

10/2/08, 4:30 PM #9

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Re: Great minds think alike ;-)

I set it up just a little different, but got the same answer.

I used E as the amount the escalator moved and got:

36-E=2(27-E). Solve for E and get 18, so the length is the number of steps plus the amount of Escalator movement or 36+18=54

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: Escalator Puzzle

10/2/08, 6:10 PM #10

Alex Yeilding
Guest

Another way of looking at it

You guys are too good! My plodding ways got me there, too, but with much more pain.

Here's an elegant view:

Consider the point in time at which Frank reached the top. He has taken 36 steps, so Sam has taken 18, and being 18 steps behind Frank is 18 steps from the top. In the rest of his trip, Sam takes 9 steps to cover that 18 steps of height. So we know that the height covered by Sam is twice the number of steps he takes. 2*27 = 54.

Escalator Puzzle

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