Tuesday Puzzle

4/21/09, 10:23 AM #1

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Tuesday Puzzle

Three people (A, B, and C) need to cross a bridge. A can cross the bridge in 10 minutes, B can cross in 5 minutes, and C can cross in 2 minutes. There is also a bicycle available and any person can cross the bridge in 1 minute with the bicycle. What is the shortest time that all men can get across the bridge? Each man travels at his own constant speed.

- - -

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: Tuesday Puzzle

4/21/09, 1:10 PM #2

Alex Yeilding
Guest

too easy or too tricky?

On first reading, I thought this was too easy. Looking for another interpretation, I came up with the answer that would be gross with another two pairs of seconds.

Re: Tuesday Puzzle

4/21/09, 1:31 PM #3

John Veerkamp,Western Mo
Guest

Re: Tuesday Puzzle

Alex may be right, this sounds too easy, but then I'm just a B student.

Re: Tuesday Puzzle

4/21/09, 2:01 PM #4

Bill Earl
Member
Offline
948 posts

Registered: 6/17/05

Re: Tuesday Puzzle

Unless I misunderstood his answer, I got 100 more than Alex.

Re: Tuesday Puzzle

4/21/09, 2:23 PM #5

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

don't think so (hint)

No, if I am reading you right. Assume that the answer has all three getting to the other side at the same time.

- - -

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: Tuesday Puzzle

4/21/09, 2:26 PM #6

Thomas Skaggs
Guest

Dan......

....one question....is it a mountain bike or a road bike? Thanks in advance. Tom

Re: Tuesday Puzzle

4/21/09, 3:05 PM #7

Larry Barrett
Member
Offline
1,070 posts

Registered: 3/11/04

Re: Tuesday Puzzle

Assuming I understand Alex's answer, my answer is Alex + 32 and a fraction (or Bill - 67 and a fraction).

Re: Tuesday Puzzle

4/21/09, 3:25 PM #8

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Re: Dan......

It was one of those single speed cruisers.

- - -

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: Tuesday Puzzle

4/21/09, 7:20 PM #9

Steven Antonucci
Member
Offline
7,941 posts

Registered: 1/21/10

I get 5 minutes

C rides the bike while A starts walking. A then bikes back 2 minutes after he started (3 minutes), and give the bike to B. A then walks back in 2 more minutes for a total of 5?

Unless there is a basket on the handlebars, and any two of the people are small enough to fit in it, then everyone crosses on the bike in 1 minute...

Re: Tuesday Puzzle

4/21/09, 8:40 PM #10

Alex Yeilding
Guest

Tricky answers:

1) 1 minute. The question stated times for "persons" to cross, but asked about fastest time for "all men" to get across. (I do learn from my own puzzles ;-) ) If there were no man, there would be no answer. One man takes the bike across, and "all the men" wait for the women on the other side.

2) 1:48. "Men" implies plural. A is the only woman. B rides 80% of the way across the bridge, in 48 seconds, and leaves the bike and walks the remaining 1/5 in a minute. C walks 80% of the way across the bridge in 1:36, then hops on the bike to finish the trip in 12 more seconds.

3) 2:20. This is the answer I originally gave, thinking that the trick only required that all three reach the other end, not that they stay there. A rides to the other end (1:00), then back to B at the 1/3 way point (0:40). B rides to the other end (0.40), and finds that C has already arrived. Now, they have all REACHED the other side, but A didn't stay, and is now back near the middle of the bridge.

But now to work it out given Dan's hint!

Re: Tuesday Puzzle

4/21/09, 9:42 PM #11

Alex Yeilding
Guest

Close to yours, Larry

I THINK I have the solution right, but am very suspect of my algebra. My answer is a weird fraction, about 3 seconds more than yours. Maybe a spreadsheet to check my arithmetic...

Re: Tuesday Puzzle

4/21/09, 10:08 PM #12

Alex Yeilding
Guest

Ugly answer

I get 3:02.26.

No, I don't think it is right. The fractions are too ugly. I must be doing something wrong. :-(

Re: Tuesday Puzzle

4/22/09, 12:43 AM #13

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

It is an ugly fraction

But not quite that one I don't think. I will post what I got for an answer and see if you can shoot holes in it.:

- - -

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: Tuesday Puzzle

4/22/09, 12:44 AM #14

Dan Donaldson
Member
Offline
5,264 posts

Registered: 9/17/01

Answer

At least as I figured it ;-)

A's speed is 1/10 (in bridges per minute), B's speed is 1/5, C's speed is 1/2, and the bicycle's speed is 1.

The fastest way I found to get everyone across is for B and C to start out on foot and A to start out with the bicycle. At a point y A will get off the bicycle and walk the rest of the way. Eventually C will get to the bicycle abondoned by A, then ride backwards to a point x, leaving the bicycle there, then turning around and walk until he reaches the end. Person B will walk until he reaches the bicycle left by C and then ride the rest of the way.

Below are the times that each will take to cross, in terms of x and y:

A: 1*y + 10*(1-y)

B: 5*x + 1*(1-x)

C: 2*y + (y-x) + 2*(1-x)

Next equate these equations: 10 - 9y = -3x + 3y + 2 = 4x + 1.

To solve set up two linear equations:

10 - 9y = -3x + 3y + 2 -> 3x - 12y = -8

10 - 9y = 4x + 1 -> 4x + 9y = 9

Then solve for x and y:

x = 12/25, y=59/75.

Given these points it will take each person 73/25 = 2.92 minutes to cross.

- - -

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: Tuesday Puzzle

4/22/09, 1:12 AM #15

Larry Barrett
Member
Offline
1,070 posts

Registered: 3/11/04

Re: Answer

Dan

I agree completely with your reasoning, and with your equations. I made an error in how I expressed the distance that C rode back, which resulted in error in my answer. I believe your answer is correct. Good puzzle.

Re: Tuesday Puzzle

4/23/09, 12:56 AM #16

Alex Yeilding
Guest

Good problem

I assumed that the minimum would be with maximum use of the bicycle, so I had C ride the bicycle back until he met up with B. Then B took the bike, and left it near the end of the bridge, where A picked it up again for the last leg. But my time was a little longer than yours. I did my algebra on intervals of time rather than distances.

But I still stand by my "one minute" answer! ;-)

Tuesday Puzzle

Posts