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
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.
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 email@example.com.