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 Post subject: I need help setting this up.Posted: Mon, 16 Apr 2012 04:56:22 UTC
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Joined: Mon, 16 Apr 2012 04:40:35 UTC
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A man in a rowboat at point P 6 miles from shore desires to reach point Q on the shore at a straight-line distance of 10 miles from his present position. If he can walk 4 mph and row 3 mph, at what point L should he land in order to reach Q in the shortest time?

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 Post subject: Re: I need help setting this up.Posted: Mon, 16 Apr 2012 06:03:30 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
jsucal wrote:
A man in a rowboat at point P 6 miles from shore desires to reach point Q on the shore at a straight-line distance of 10 miles from his present position. If he can walk 4 mph and row 3 mph, at what point L should he land in order to reach Q in the shortest time?

What have you tried?

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 Post subject: Re: I need help setting this up.Posted: Mon, 16 Apr 2012 21:39:03 UTC
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Joined: Mon, 16 Apr 2012 04:40:35 UTC
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I know that the distance of the shore is 11.66 miles and that i will divide the rowing time by 3 and the walking time by 4 and i know that i have to set up an equation but don't know what to use.

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 Post subject: Re: I need help setting this up.Posted: Mon, 16 Apr 2012 22:42:38 UTC
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jsucal wrote:
I know that the distance of the shore is 11.66 miles and that i will divide the rowing time by 3 and the walking time by 4 and i know that i have to set up an equation but don't know what to use.

Whoa, I thought the shore distance was 6, why is it now 11.66?

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 Post subject: Re: I need help setting this up.Posted: Tue, 17 Apr 2012 01:24:44 UTC
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Joined: Mon, 19 May 2003 19:55:19 UTC
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Location: Lexington, MA
Hello, jsucal!

You've twisted some of the facts . . .

Quote:
A man in a rowboat at point P 6 miles from shore desires to reach point Q on the shore
at a straight-line distance of 10 miles from his present position.
If he can walk 4 mph and row 3 mph, at what point L should he land in order to reach Q in the shortest time?

Code:
P o
| * *
|   *   *    10
6 |     *     *
|       *       *
|         *         *
o-----------o-----------o
R     x     L    8-x    Q
: - - - - - 8 - - - - - :

The man is at
is 10 miles from
Using Pythagorus:

He will row to point
. . Let .Then
Then he will walk to point
. .

He will row miles at 3 mph. . This will take hours.
He will walk miles at 4 mph. . This will take hours.

His total time is: .

And that is the function you must minimize.

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