Fastest Route to Reach Blonde on Beach: 400/3 m

[leprofece]

390) a young man this boat 100 m from a straight coast where you can see a blonde lying down on the beach at 150 m from the point more close to the young man. If this can paddle at a speed of 4 m/sec and walk to 5 m/sec, at that point you should dock pars to reach the site where the blonde is in the shortest possible

answer is 400/3 from the point closer o more close to the beach

I think is the same situation as the another one that I put 5 minutes ago

 

[Prove It]

390) a young man this boat 100 m from a straight coast where you can see a blonde lying down on the beach at 150 m from the point more close to the young man. If this can paddle at a speed of 4 m/sec and walk to 5 m/sec, at that point you should dock pars to reach the site where the blonde is in the shortest possible

answer is 400/3 from the point closer o more close to the beach

I think is the same situation as the another one that I put 5 minutes ago

Yes it is exactly the same. Use what I posted in the other thread to see if you can set up this problem correctly.

 

[soroban]

Hello, leprofece!

Did you make a sketch?

A young man in a boat 100 m from a straight coast where he sees a blonde
lying down on the beach at 150 m from the point closest to the young man.
If he can paddle at a speed of 4 m/sec and walk to 5 m/sec, at what point
should he dock to reach the blonde in the shortest possible time?

Answer is 400/3 m from the point closest on the beach.

    M o
      | *
      |   *    _______
   100|     * √x²+100²
      |       *
      |         *
      o-----------o-------------o
      A     x     P   150-x     B
      * - - - - - 150 - - - - - :

The man is at $M\!:\;MA = 100$

The blonde is at $B\!:\;AB = 150.$

He will row to point $P\!:\;AP \,=\,x$
Then he will walk to $B\!:\;PB = 150-x$

He will row $\sqrt{x^2+100^2}$ m at 4 m/sec.
$\quad$ This will take: $\:\frac{\sqrt{x^2+100^2}}{4}$ seconds.

He will walk $(150-x)$ m at 5 m/sec.
$\quad$ This will take $\:\frac{150-x}{5}$ seconds.

His total time is: $\:T \;=\;\frac{\sqrt{x^2+100^2}}{4} + \frac{150-x}{5}$ seconds.

And that is the function you must minimize.

 

[leprofece]

Ok I did it in another way and I got 32,63
Then I introduce in distance{\sqrt{150^2-(100-32,63)^2}}
And I got the right answer
Am I Correct??'Second There is a program called math type
May I Use this program to solve my typing problems?

Id apreciatte your helping me

 

[MarkFL]

Ok I did it in another way and I got 32,63
Then I introduce in distance{\sqrt{150^2-(100-32,63)^2}}
And I got the right answer
Am I Correct??'Second There is a program called math type
May I Use this program to solve my typing problems?

Id apreciatte your helping me

You need to enclose your $\LaTeX$ code with tags or delimiters so that it is readable (such as the MATH tags). I am not familiar with math type. Have you tried using the tools we provide to create your $\LaTeX$?

 

[leprofece]

yes but i have never got it
if i write sqrt x
it appears \sqrt{x} now, what can i do to appear like you?

 

[MarkFL]

yes but i have never got it
if i write sqrt x
it appears \sqrt{x} now, what can i do to appear like you?

You could use:

[noparsetex]\(\displaystyle \sqrt{x}\)[/noparsetex]