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## #1 2017-03-12 02:11:06

CIV
Member
Registered: 2014-11-09
Posts: 69

### Help with an optimization problem.... please.

It's the rowing and walking problem.

Basically, you're 4 miles out at sea from the closest point on shore and from that point on shore is a restaurant 6 miles away. You row at a speed of 2mi/hr and walk at a speed of 3mi/hr.

A: At what point on the shore should you land to minimize the travel time.

B: If you walk at a speed of 3mil/hr, what's the minimum speed at which you should row so that the quickest way is to row directly.

Now I already searched online for help and I got the answer to part A, which is:

miles from the closest point on shore towards the restaurant.

I calculated the quickest travel time as well:

I compared the quickest time with the limits of the interval, that being 0 and 6. When x = 0, T = 4 hours. When x = 6, T is about 3.61 hours.

Now... the second part has me pulling my hair out because I feel like it's such an easy thing to figure out, but I'm not getting what the book has listed as the answer:

So, what I know is that you will be rowing a distance of:

miles

I also know that the quickest travel time is:

So what I need now is the rate at which you must row.

If I use my answer to calculate total direct rowing time I get about 3.49 hours which is what it was before with some rowing and walking. This is the MINIMUM rowing rate. If I use the answer in the book I get 2.88 hours????

Am I missing some here? Is the answer in the book wrong? Did I not understand the question? I wrote part B here just about word for work just in case I misunderstood. I thought it was weird when it read "If you walk at a speed of 3mi/hr", because what does that have to do with the minimum rowing speed for rowing directly to be the fastest route.

Thanks everyone.

Last edited by CIV (2017-03-12 13:43:46)

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## #2 2017-03-12 07:30:54

bob bundy
Registered: 2010-06-20
Posts: 8,232

### Re: Help with an optimization problem.... please.

hi CIV,

Haven't tried part 2 yet because I'm not getting the same as you for part 1.

I get

edit: Just calculated quickest time with the above value and I get your result.  So I'll assume that was a typo and plough on.   Watch this space.

Further edit:

Call the velocity V.  Then the time is

Set that equal to your previous minimum time.  I found it simplified a lot and I got:

Hope that helps.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #3 2017-03-12 13:45:38

CIV
Member
Registered: 2014-11-09
Posts: 69

### Re: Help with an optimization problem.... please.

You're right, it was a typo. I don't understand what you did and what you got isn't what the book has as the answer:(

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## #4 2017-03-12 20:32:17

bob bundy
Registered: 2010-06-20
Posts: 8,232

### Re: Help with an optimization problem.... please.

hi CIV,

Looking again at your working, it seems we are using a different interpretation of part 2.  2 root13 is the distance across the sea from start to finish.  So you aren't making any use of the walking speed.  I thought the question meant row straight to the shore, as quickly as possible, and then walk 6 miles along the shore.  I assumed this as part 2 repeats the walking speed.  Why say this if no walking is involved?

Anyway, let's go back to part 1 first.  Is the answer we both have considered to be correct by the book?

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #5 2017-03-13 00:28:45

CIV
Member
Registered: 2014-11-09
Posts: 69

### Re: Help with an optimization problem.... please.

bob bundy wrote:

hi CIV,

Looking again at your working, it seems we are using a different interpretation of part 2.  2 root13 is the distance across the sea from start to finish.  So you aren't making any use of the walking speed.  I thought the question meant row straight to the shore, as quickly as possible, and then walk 6 miles along the shore.  I assumed this as part 2 repeats the walking speed.  Why say this if no walking is involved?

Anyway, let's go back to part 1 first.  Is the answer we both have considered to be correct by the book?

Bob

Yes. The answer for part 1 is correct. I corrected my typo.

Ok so yea I didn't type out part b word for word because I thought what I wrote was pretty clear, but that OK. Here's exactly what part b says:

If she walks at 3 mi / hr, what is the minimum speed at which she must row so that the quickest way to the restaurant is to row directly (with no walking)?

That's word for word. I probably should of said row directly to restaurant:/ Now you see what I mean about the book mentioning walking speed for part b? I know the distance to the restaurant directly by sea is 2 root 13 and I know what the quickest time is, so all I need is the rate at which to row to at least achieve the quickest time. That would be the minimum rate at which to row, which really isnt all that much faster than the original 2 mi / hr rowing speed.

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## #6 2017-03-13 00:42:14

bob bundy
Registered: 2010-06-20
Posts: 8,232

### Re: Help with an optimization problem.... please.

hi CIV,

Now I'm getting exactly the same as you.  What does the book say for an answer?

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #7 2017-03-13 04:06:06

CIV
Member
Registered: 2014-11-09
Posts: 69

### Re: Help with an optimization problem.... please.

The book has this as the answer:

This book doesn't usually have wrong answers so Im really trying to exhaust myself here to make sure it's not me.

Again, the book has 8 / root 5 as the answer to part one too. LOL. So I'm really scratching my head here.

Last edited by CIV (2017-03-13 04:08:18)

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## #8 2017-03-13 05:20:33

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Help with an optimization problem.... please.

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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## #9 2017-03-13 05:26:32

CIV
Member
Registered: 2014-11-09
Posts: 69

### Re: Help with an optimization problem.... please.

I just solved another optimization problem, part a of this problem,  on my own without any help, except checking my calculations online. I didn't google the actual problem to see how its set up. Totally got it right and I'm so happy. Totally awesome:)

The problem: If you had a piece of wire 60 units in length, where would you cut this wire to form a square and a circle with A: the minimum combined area and B: the maximum combined area.

It involved making calculations with pi, it was confusing me a bit. Im not used to working with something like 2(pi)x as a term. Just need to solve for the max now.

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## #10 2017-03-13 16:10:02

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Help with an optimization problem.... please.

Yes. I am getting

continuing with my previous post#8

Last edited by thickhead (2017-03-13 16:10:31)

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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## #11 2017-03-13 18:05:37

CIV
Member
Registered: 2014-11-09
Posts: 69

### Re: Help with an optimization problem.... please.

Yes. I am getting

continuing with my previous post#8

How did you get 9 / root 5? I don't understand what you mentioned.

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## #12 2017-03-13 18:17:21

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Help with an optimization problem.... please.

I think my solution is clear 9/sqrt(13) matching with your book answer.I never mentioned 9/sqrt(5).And what you did not understand?My post no.8 or the answer?

Last edited by thickhead (2017-03-13 19:24:05)

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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## #13 2017-03-13 22:02:27

bob bundy
Registered: 2010-06-20
Posts: 8,232

### Re: Help with an optimization problem.... please.

Sorry for being a bit slow, but I cannot follow how

Would you mind filling in the missing lines.  Thanks,

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #14 2017-03-14 02:24:59

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Help with an optimization problem.... please.

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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## #15 2017-03-14 02:40:35

bob bundy
Registered: 2010-06-20
Posts: 8,232

### Re: Help with an optimization problem.... please.

Many thanks.  Got it now!

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #16 2017-03-14 16:06:03

CIV
Member
Registered: 2014-11-09
Posts: 69

### Re: Help with an optimization problem.... please.

I meant 9 / root 13. I still don't follow what your doing there.

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## #17 2017-03-14 17:15:23

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Help with an optimization problem.... please.

The point is the quickest time calculated on the basis of rowing speed of 2 mi/hr is not valid now since the rowing speed has changed. Now i want to know how you handled the first part so that I can continue from that.It won't help if the 2 parts are disjoint.

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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