Do You Need Math to get into Heaven?

Clearly, nothing is more important than math. The cartoon above is all the proof of this statement that is needed.

(In case you can't read the caption, St. Peter is asking the potential Heaven candidate, "Now the last thing you have to do to get into Heaven is to answer this question: Two trains left Chicago traveling 40 mph in opposite directions and ...").

So, yes, a reasonable knowledge of mathematics is needed to get into Heaven. So as a courtesy to my beloved readers, I have decided to show you how to do such math, so that you will not have to go to “that other place” just because you forgot your Algebra II.

NOTE: don’t stop reading now! This article is written for math-phobics, and anyone else who has not used Algebra since the last century.

So let’s get to it. Here’s the math problem we’re going to solve. Even I didn’t like these kinds of problems when I first studied Algebra. This should encourage you to continue reading.

“Boston and New York City are about 200 miles apart. A train leaves Boston for New York at a speed of 40 mph. Another train leaves New York for Boston at a speed of 60 mph. How long will it take for them to meet?”

(If they are on the same track, they’ll do a bit more than “meet”, but we are a peaceful people, so let’s leave it at that.)

Of course, you can whip out your calculator and keep guessing until you get the answer. Actually, mathematicians and scientists do a lot of guessing, so there is nothing wrong with this. But here we want to use Algebra, because it is such a nice word. In case you didn’t know, Algebra comes from an Arabic word meaning Unknown.

So where to start on this problem? I’d draw a simple picture, just to postpone actually having to solve the problem.

             -------> 40 mph                 60 mph <-------

Boston o-----------------------------------------------------o New York

                                     200 miles


Leonardo da Vinci could not have drawn a better picture.

There is one big secret to solving algebraic equations: let a variable (usually a letter of the alphabet) represent the unknown value you are trying to find. In this case, it is the time it takes for them to meet. Let’s write this down.

Let T = the time it takes for the two trains to meet.

And another realization is that the time each train travels before they meet is the same, so we only need this one variable for time.

One other piece of knowledge needed is one you all know, D = RT, which stands for Distance = Rate x Time. Yes, you know this and use it all the time. If I said a car was traveling at 50 mph for 3 hours, and asked how far it went, you’d multiply these numbers (the rate or speed of the car and the time it traveled) to get 150 miles.

Here’s the most fun part, and the hardest as well. Both trains travel at different rates, so we need to apply this equation for each train.  So:

Let DB = the distance the train from Boston travels before it meets the New York Train.

Let DN = the distance the train from New York travels before it meets the Boston Train.

Applying the D = RT formula to both trains, we get:

DB = 40T (Note that since T is the same for both trains, we don’t need to indicate its origination point.)  And we get:

DN = 60T

Now what?  We'll if you look back at the problem, you'll notice that we didn't use one of hte facts given there, namely that the distance from Boston to New York is 200 miles. Writing this algebraically:

DB + DN = 200

Now we replace each of these distances with the right hand side of the two equations above:

40T + 60T = 200

Alright, you’ll have to remember a little Algebra to simplify this equation. Since I’m hungry, I’ll use a food analogy. If you had 40 apples and 60 apples, you’d have 100 apples. (If you hungry now and need to go eat, please do so but come back.  And don't forget your New Year's resolution to lose weight this year.)

Therefore, 40T + 60T = 100T. So we put this on the left side of the above equation to get:

100T = 200

My more intelligent readers will immediately realize that T = 2 hours, and there you have it!

Of course, we must check our work. We would never think about not checking our work!

If the train leaving Boston traveled for 2 hours at 40 mph, it would travel 80 miles. If the train leaving New York traveled for 2 hours at 60 mph, it would travel for 120 miles. Since 80 miles + 120 miles = 200 miles, which is the distance between the cities, our answer checks.

So now, gentle reader, there are no math obstacles for you getting into Heaven. St. Peter will be quite proud of you.

By the way, here’s one last equation for you:

Math = Heaven

Trust me on this.

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Tim Farage is a Senior Lecturer in the Computer Science Department at The University of Texas at Dallas. You are welcome to comment upon this blog entry and/or to contact him at tfarage@hotmail.com.

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The Dallas Cowboys and Math Phobia

If you like The Dallas Cowboys but you don't like math, this article is guaranteed to make you like math. Well, at least you'll see the purpose in being able to solve two simultaneous equations in two unknowns. Wait! Don't stop reading yet. By the time I'm through, it's possible that you might actually understand that some of the stuff you learned and (probably forgot) in Algebra II.

Here's what we're going to do. Given some stuff that's found in most major newspapers, we're going to determine something interesting about the score of The Dallas Cowboys vs. The Carolina Panthers game on Monday, September 28, 2009. If you're reading this after the game, keep reading anyway.

If you look in your paper for the games in the upcoming week, there's usually some information about each upcoming game. For instance, I'm writing this the Thursday before the game and here's what is has:

Favorite: Dallas
Underdog: Carolina
Today's Line: 9
O/U: 47

So what does this mean? The 9 is called 'The Line' and it means that Dallas is expected to win by 9 points. (To be technical, Las Vegas sets 'The Line' so that half the bettors bet on the Cowboys and the other half bet on the Panthers. The rub is that if you bet on the Cowboys, you'll only win if the Cowboys win by more than 9 points). So let's express this with a mathematical equation.

Let X = the Cowboys final score and let Y = the Panthers final score. Then 'The Line' predicts that:

X – Y = 9 (i.e. the Cowboys will win by 9).

Now O/U stands for Over/Under, and that just means that the total score of both the Cowboys and Panthers is expected to be 47 points. So if you bet the 'Over' you'll win your bet if the total score is more than 47 points. The math equation for this is fairly simple as well:

X + Y = 47

Let's put these equations together so we get what mathematicians call two simultaneous equations in two unknowns.

X – Y = 9
X + Y = 47

Now each of these equations separately has lots of solutions. For example the first equation has a solution X = 100 and Y = 91.

The second equation also has a number of solutions, for example, X = 30 and Y = 17.

But what if I asked you for a value for X and a value for Y that satisfy BOTH of the equations. If you found these values, you just solved two simultaneous equations in two unknowns. There are math techniques that allow one to solve these, but you can try to do so by guessing.

Did you get a solution? Not to worry, because here it is:

X = 28 and Y = 19. Note that their difference is 9 and their sum is 47, just what the equations called for.

Now you're going to ask, 'Who cares, and what does this mean anyway?'.

What this means is that the most likely score of the game is:

Cowboys 28
Panthers 19

Don't get me wrong. It is NOT likely that this will be the final score; it's just that this is the most likely score. So if you go to Vegas and had to bet on a final score, this score would have the best chance of winning.

Now don't pick up the phone and call your bookie. Vegas in the long run always wins, so you'll just be throwing your money away. I'm not much of a betting man myself, except that I irrationally spend $1 per week on a Texas Lottery ticket. I do play an occasional game of Texas Hold 'Em with my nephew and his friends, but I always win, so that really isn't gambling.

OK, back to the main point. By using what's in the paper, and being able to solve two simultaneous equations in two unknowns, you can predict the final score of any football game. How cool is that?

Now repeat after me, "Math = fun."

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Tim Farage is a Senior Lecturer in the Computer Science Department at The University of Texas at Dallas. You are welcome to comment upon this blog entry and/or to contact him at tfarage@hotmail.com.
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