An Airplane Ride

For those of you who read my recent post about my 82 year old mom, this is a story that connects to that.  On September 8, I boarded a plane in the Colorado Springs airport to fly to Mobile, Alabama (Laura Hayden, who herself lives in Alabama, instructed me that this is pronounced Mo - Beel, accent on the second syllable.  This came in handy giving me some street cred in the Land of Dixie).

No sooner had we boarded the plane then the pilot came on the speaker informing us that the plane had some mechanical difficulty that had to be attended to before we could take off.  Time passed and it became obvious that this was a problem that could lead to not only delays but even a cancellation.  The flight attendants were terrific handing out drinks and smiles and letting us know they and American Airlines would do everything they could to get us to where we were going.

Now what usually happens to me is that I have multiple hour layovers in Dallas before my connecting flight to Mobile.  Not so this time.  This time I had a mere one hour layover.  When half that time had elapsed, I began to be anxious that I would miss my connection in Dallas.  

Now, I'd seen tons of movies and TV shows where some jowly bully browbeats the flight attendant telling her she needs to do something.  "Dammit, I need to be in New York by ten AM or a million dollar deal is out the window.  Do you understand, girly, girl?"

I didn't want to be that guy so I casually mentioned my situation - my 82 year old mom was in the hospital with double pneumonia - to the senior attendant.  Immediately, the entire attendant crew were at my seat with commiserating smiles and telling me they would do everything in their power to make sure I made my connecting flight.

It was then that the pilot came on the horn telling us that it might turn out that we would have to deplane and that American Airlines would get us other flights to our destinations, even if those flights were with other airlines.  

I checked my watch.  Thirty-five minutes of my hour layover had evaporated.

The attendants came back to my seat and told me I was being considered first in placement to other flights.

The pilot came back on the horn telling us the plane had checked out and we were taking off momentarily.  My attendant came again and this time squeezed my hand.

We took off and as far as I knew my fate was in the hands of the gods.  Not so.  Again, the attendant came to me.  She bent down and whispered in my ear.

"A man in first class, in the first seat, has agreed to move to another seat so that you can have the seat closest to the door."

As soon as it was safe - to move about the cabin - I quietly grabbed my luggage from the overhead bin and made my way to the front of the plane.

In all my years on the planet, I've never sat in first class.  It was pretty darn cool.

Before we landed, the attendant came to me and handed me a piece of paper with the gate of my flight.  Normally, these are announced anyway, but it was nice of this wonderful lady to keep me in her thoughts.

When we landed in Dallas, the rest of the folks in first class waited until I got my stuff and was in the aisle before they got out of their seats.  I can only guess that either she or the man who had given up his seat had told every one about my situation.

I was off and running.  It turned out my flight was in a different concourse than where I had landed.  I had to get on a train.

The gate where my plane waited was empty when I finally got there, but it looked like the folks were expecting me. I was ushered onto the flight.

As I sat down, I found myself smiling.  The world is full of marvelous, sympathetic, loving people.  

Even as write this, I have to say I am a big fan of my species.  Yay, for the human race!!!!

My Parents

For those you who are lucky enough to have one or more parents alive, this is for you.

A few years back my Dad passed away.  We didn't always get along.  In fact, we fought most of the time.  I thought he was a narrow minded old man who would get cranky at the drop of the hat.  He was opinionated, given to self pity, and didn't always treat the folks who cared for him like I thought he should.  Especially, my mom.

Of course, he had an excuse.  In 2000, he lost his sight.

He used to work on cars and was so good at it the folks in his church asked him to maintain the school buses they used to bring invalid members to church on Sundays.  I guess he did a good job of it, because when I came to Alabama for his funeral, just about everybody said that after he went blind, nobody could take his place.  But that wasn't all that they said.  They talked about how funny he was and what a good friend he could be.  Always there, even after his world went dark, with a helping hand and a joke.  Or a prayer.

You got not idea how mad this made me.  Why couldn't he show those folks he was supposed to care the most about this side of him?  And then he was gone.  He wasn't there to shout at and tell all the things I thought he should have done differently.  And after a while I didn't want to shout at him.  I just wanted him back.  With all his contrary ways, I just wanted to pack him into the passenger seat of my car and take him for a drive.  I wanted to hear him, one more time, tell me how to drive, even though he could no longer see the street lights.

And now my mom's sick.

I got a call from her sister that a few days ago, she was checked into the hospital.  And I'm mad all over again.  And scared.  My mom is 82 and even though she's one of the toughest people I've ever met (her mother lived to almost 100), she's not the mom I had growing up.  She's stooped and walks slow.  She tires easily.  She's given to tripping over things and breaking bones.  And, in her own way, she's just as contrary as my Dad was.

And it makes me crazy.

She fell a few years back over one of those stupid trapezoidal parking blocks and broke an arm.  Even though I talked to her after the fact, she never told me what had happened.  "I didn't want you to worry."  I learned the actual facts only months later.

And now she's sick.  I'll be flying back again, and I don't want to hear folks tell me what a good person she was. God Damn it.  I already know that.  She's sweet.  And generous.  And patient with a son who should call more often.  I want her to tell me how she feels.  I want to bring her home from that damn hospital.

And I want to tell her stuff.  I want to tell her that I'm glad to see her getting better.  That she looks good.  I want to sit with her, and laugh together at the things that tickle her on TV.  I want to give her a hug, and let her know that even though she drives me crazy that it's okay.

She's my mom.

This Train is Bound for Glory

LOCAL VS EXPRESS

FACTS:

LOCAL - 30 mph, 2/3 of the distance from DC to Richmond this train's speed drops to half

EXPRESS - 60mph, leaves later than Local

Express usually catches Local right at DC (total distance).  Because of difficulty, Express catches Local after 27 and 1/9 miles.

Here we go, full steam ahead:

I will used an algebraic solution, so let x be the distance Local travels from the time the problem arises to the time the Express catches up with it.  Also let the distance from DC to Richmond be one unit (this will be explained in a minute). We will now construct an equation.

Let's use our facts.  Express normally travels twice as fast as the local but after the mechanical problem it is traveling 4 times as fast.  Also since the Express normally catches the Local at the end, the Local has traveled half the distance when the Express departs.  Sooooooo, when the Local has traveled 2/3 of the distance the Express has traveled 1/3.  Thus the equation:

2/3 + x = 1/3 + 4x.

Solving

x = 1/9 of the way (remember the total distance was one unit).

Now the Local has only 1/3 of the distance still to go, therefore at the time the Express catches the Local there is 1/3 - 1/9 = 2/9.

Remember though the Express catches the Local after 27 and 1/9 miles

Dividing, we get

27 1/9 X 9/2 (invert and mutiply)

We get 122 miles from Richmond to Washington DC

Prime Numbers and The Meaning of Life

Actually, the meaning of life is 42, so now that we have that out of the way, let's solve the prime number and remainder problem.  I will offer two solutions for this tasty little puzzler.  I'll call them the Format Method and the Consecutive Integer Method.

Format Method.  First of all we need an agreement that all integers are of the following formats: 6n, 6N + 1, 6N + 2, 6N + 3, 6N + 4, 6N + 5, where N is an integer.  If we go to 6N + 6 this can be written 6(N+1) which is just another version of 6N.  I claim 6N + 1 and 6N + 5 are the only possible primes (having exactly 2 divisors, 1 and itself).  6N is obviously divisible by 6.  6N + 2 is the sum of 2 even numbers thus even and divisible by 2, as is 6N + 4.  6N + 3 is the sum of two numbers divisible by 3 thus divisible by three itself. Therefore we only need consider 6N + 1 and 6N + 5.

Now onto our problem:

Square them:

36N^2 + 12N + 1 or 36N^2 + 60N + 25

Add 17

36N^2 + 12N + 18 or 36N^2 + 60N + 42

With a minimum of algebra we get:

12(3N^2 + N + 1) + 6 or 12(3N^2 + 5N + 3) + 6

Dividing by 12 we can see that both these numbers leave a remainder of 6.

Consecutive Integer Method.  Let P be our prime number bigger than 3

Square it: P^2

Add 17: P^2 + 17

Rearranging algebraically we get: (P^2 - 1) + 18

Now factor.  (P - 1)(P + 1) + 18

Here's where consecutive integers comes in.

P - 1, P, P + 1 are consecutive integers (for example if P is 11 the we get 10, 11, 12)

Therefore either P + 1 or P - 1 is divisible by 3

And because P itself is odd (all prime numbers bigger than 3 are odd) then both P - 1 and P + 1 are even and (P - 1)(P + 1) is divisible by 4.  Thus (P - 1)(P + 1) is divisible by 12.

Sooooooo (P - 1)(P +1) + 18 when divided by 12 leaves a remainder of 6 (we need only consider what happen when we divide 18 by 12).