Puzzle - Cow in the Bridge Escapes Train

Problem:

A cow is standing 5 feet from the middle of the bridge.
A train is coming towards the cow at speed of 90 miles per hour from the near end
(Note #1) Distance between the near end of the bridge and the train is twice as long as the bridge.
If the cow had tried to move forward in the same direction as of the train then the cow would have got hit by (Note #2) three inches.
But it moved in opposite direction to the train and saved by one feet.
Then What is the length of the bridge and The velocity of the cow?

This problem is misquoted in many websites and forums.
#1 "Distance between the near end of the bridge and the train is twice as..." is misquoted as "the train is twice as..."
#2. "three inches" is misquoted as "three feet" or "one feet".

My source is Mathematical puzzles of Sam Loyd, Volume 2 By Sam Loyd, Martin Gardner Page 117. I saw this version in Google Book Review of this book.

Step by Step solution:

T...........................1...A........C...M........2...B

T = Position of the train just before cow moved
C = Position of the cow just before cow moved
A = Nearer (to train and cow) end of Bridge
B = Far (to train and cow) end of the Bridge
1 = Position of the train just after cow escaped. [Note: Cow did not go to 1; it escaped at A] (If cow moved towards train)
2 = Position of the train just after cow was hit (If cow moved towards far end)
M = Mid point of Bridge
Cv = Speed (V=Velocity) of the cow
Tv = Speed (V=Velocity) of the train

Let us assume length of the bridge AB is 2x
Assuming 2x rather than x makes it easier to calculate, as we need to deal with midpoint based calculation.
And, let us calculate distance traveled
T1 = TA - A1 = 2 times AB - 1 = (4x - 1)
T2 = TA + A2 = 2 times AB + AB - B2 = 3 times AB - 0.25 = 6x - 0.25
Similarly
CA = AM - CM = (x - 5) = x - 5 [Note: Cow did not go to 1; it escaped at A]
C2 = CB - B2 = CM + MB - B2 = 5 + x - 0.25 = x + 4.75
Time taken by Cow / Train is same in a given option.
CA / Cv = T1 / Tv ...(1)
C2 / Cv = T2 / Tv ....(2)
Adding (1) and (2)
(C2 + CA) / Cv = (T1 + T2) / Tv
i.e.
Cv = Tv * (CA + C2) / (T1 + T2)
Cv = 90 * (2x - 0.25) / (10x - 1.25) = 90 / 5 = 18 mph is the speed of the cow

Subtracting (1) and (2)
(C2 - CA)/Cv = 9.75ft/18mph = (T2 - T1)/Tv = (2x + 0.75) ft/90mph
i.e. 2x + 0.75 = 48.75 ft or 2x = 48 ft is the length of the bridge AB

Variation 1: CM is not given and asked to find out just Cv.

There is no change in Train related calculation. But
CA = AM - CM = (x - d) = x - d
C2 = CB - B2 = CM + MB - B2 = d + x - 0.25 = x + d - 0.25
So, C2 + CA is still the same; 2x - 0.25. So, Cv is still 18

Puzzle - Escalator

There are couple of variations for Escalator Puzzle. I picked this from the net. Source says it is Puzzle no 27 of PUZZLES TO PUZZLE YOU by Shakuntala Devi.

Here is the problem statement:

QUOTE
I walk down the escalator. If I walk 24 steps I require 34 min. If I walk down 36 steps I need 26 min. What are the no of steps on the escalator.
UNQUOTE

Here is the step by step solution:

(01). Let us try to get an equation here. No obvious equation.
(02). Let us look at facts not stated explicitly. "Escalator"
(02a) . Escalator speed will be same in both cases
(02b) . If Escalator had e steps, when I moved p steps, escalator moved the rest (e-p) steps.
(02c). And it did so, in the time "I needed to walk".
(03) We have the equation: (e-24) /34 = (e-36)/26 = Elevator speed = Steps/Minute
(04) Number of steps, e = 75
(05) Elevator speed is 1.5 steps per minute....

REMEMBER: Escalator movement matters, not your movement.

PS:
When I first solved the escalator problem (variation of this problem) in Infosys (INFY) test in Feb 1992, I did not have a clear idea about how an escalator worked. Seen it only once in Bengaluru. Not that mattered.

Monitor goes off and on

One fine day, just hours before deadline to file my taxes, my PC monitor started giving me trouble.
It would go off ( as if it was turned off) and on ...
Interval is different each time.
Could not say what caused it..
Even though I remembered touching monitor menu setting to change brightness...

Searched internet ... Did not find much and except the information about similar problem when it is next to different devices with thermostat.

My case was ... Problem just started ... Not new connection ... Not new PC or Monitor

Finally, I remembered that while setting brightness, there was some menu that showed "Analog" and "Digital". So, tried changing "input source' to "Digital", and problem went away...

I have no explantion (Dont have one!!!)

Intro!!

Hi:

I am going to write about everything I know, heard of, tried out, found by luck that helped me.
Will give credit to my source.
Forgive me if my source is not the original source

I have created this blog, assuming "this might help you!"

uunaashe