On Sun, 06 Apr 2008 15:17:30 -0400, RKL <maryjim@[EMAIL PROTECTED]
> wrote:
>Here's an interesting one:
>
>A lifeguard stationed on a beach with a straight shoreline sees a
>swimmer in trouble 150 meters down the beach and 60 meters out in the
>water.
>
>The lifeguard can run 8 m/s on the beach and swim 2 m/s in the water.
>
>What path down the shoreline and out into the water should the
>lifeguard take to reach the swimmer in the SHORTEST AMOUNT OF TIME?
To rephrase, the lifeguard should run some distance x down the beach
(where 0 <= x <= 150) and then swim the remaining distance to the
swimmer. At what value of x is the time spent a minimum.
In terms of x, how far down the beach did the lifeguard run? In terms
of x, how long did it take?
In terms of x, what is the distance across the water to the swimmer?
How long will it take to swim that distance?
The total time is obviously the sum of the two times above. What is
the standard method for determining where a function has a local
minimum?
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