Saving The Mayor (Part 2)

– Saving the Mayor, Part 2 –

To play Part 1, click this link- Find the Cell Number, free the Mayor

PART 2 – Saving the Mayor (Again....)

It’s another cold day off the East of France. It was as if a supernatural presence had manifested in the skies above as thunder roared and thin, wispy clouds eerily floated through the sky. An agonizing scream escaped into the air, falling on deaf ears. The only one that would hear his plea was the room that had now become his place of imprisonment.

—The Note—

“Detective Flint, there’s a note on your table” Charlie gently reminded, keeping Flint’s great temper in mind. “Merci Charlie, I’ll be there in a second," Flint quickly replied. Flint walked over to his office, and when he saw a special red envelope on this table, his jaw dropped to the floor. “You again?” he said, partly flabbergasted. “This means the Mayor has been kidnapped a second time,” he continued, burying his face in his hands. He slides a crumpled paper out of the envelope. It reads:

There’s another red envelope with a crumpled paper inside, this one is similar.

He had written this in small handwriting on the bottom of the page: Whoever knows where our paths may cross? Maybe it’s here you will find the Mayor.

Flint opened the third and final envelope, to find two things inside.

Where is the Mayor and which train should you catch?
NOTE THAT EACH DOT REPRESENTS THE DESTINATION OF THE TRAIN AND ITS NUMBER, ONE DOT HAS NO CORRELATION TOWARDS THE OTHER DOTS

• Weekends are slow days here on PSE. As of now, your question has gotten just 28 views. Have patience. – M Oehm Jul 22 '17 at 13:11
• "It’s another cold day off the East coast of France" East is about the only direction France doesn't have a coast in, unless you count the banks of the Rhine as coast. – M Oehm Jul 22 '17 at 13:12
• @MOehm Thanks for the info. Will just change it to East. – Riddle Me This Jul 22 '17 at 14:11
• @BrownEyedNinja don't self answer until several weeks have passed, not days – Beastly Gerbil Jul 22 '17 at 15:03

The mayor is in

Lorraine.

And you should take train

#ff0000

Why?

The papers can be solved to give two equations for a line, and they intersect at (22.84, 23.74) - which matches to Lorraine on the map. The red dot with colour value #ff0000 is at place (23, 24) so you should take that train.

Paper 1:

Y:

We can use the Pythagorean theorem ($a^2+b^c=c^2$) to find y.

$5^2+12^2=c^2$
$c^2=169$
$y=13$

X:

area of a triangle = $0.5bh$. Base = 12, Height = 12.
$0.5*5*12 = 30$ so $x = 30$

C:

The equation of a line is $y=mx+c$.
$y=13$, $m=-1.5$, $x=30$
$13=-1.5*30+c$
$13=-45+c$
$c=45+13$
$c=58$

Line equation 1:

$$y=-1.5x+58$$

Paper 2:

X:

x is the area of the rectangle, 5*4=20.

Y:

$v$ (volume of cylinder)$= π*r^2*h$
$h=40$,$v=125$
$125=π*r^2*40$
$125/40/π=r^2$
$0.99=r^2$
$y≈1$

C:

$y=mx+c$
$y=1$, $m=8$, $x=20$ $1=8*20+c$
$1=160+c$ $-159=c$

Line equation 2:

$y=8x-159$

Plotting

1: y=-1.5x+58
2: y=8x-159

Intersection = (22.84, 23.74)

This matches the map at

Lorraine

And gives train number

#ff0000

• Eh, c=1-160=-159. You don't divide that. – Sid Jul 22 '17 at 15:37