# Marathon Math – The Math Behind the Houston Marathon

Tomorrow I attempt to finish my first marathon. There’s a 6 hour limit to finish, which makes me think about the math behind the marathon!

Assuming I run a steady 13:45 minute/mile pace for the whole 26.2 miles, I’ll finish exactly in the 6 hour time limit.

But of course my pace will vary. I’ll be faster at first. And I’ll likely want to crawl across the finish line.

So how fast do I need to go at the beginning so I can go as slow as possible at the end?

### I’ll start the marathon fast.

Without a backpack (which I wear running to work), I can do about a 10:30 minute/mile pace.

So here’s the math problem: If my first mile is at 10:30 and my last mile averages with the first to be 13:45, what will my last mile be?

10:30 = 10.5 minutes
13:45 = 13.75 minutes

(10.5 + last mile pace)/2 = 13.75

So the last mile pace = 17 minutes per mile!

Holy cow! I totally can do this!

### I’ll slow down gradually.

If I go from 10:30 min/mile to 17:00 min/mile for the last mile, what should the pace be for each mile in between?

Mile # => Pace
1 => 10:30
2 => 10:45
3 => 11:00
4 => 11:15
5 => 11:30
6 => 11:45
7 => 12:00
8 => 12:15
9 => 12:30
10 => 12:45
11 => 13:00
12 => 13:15
13 => 13:30
14 => 13:45
15 => 14:00
16 => 14:15
17 => 14:30
18 => 14:45
19 => 15:00
20 => 15:15
21 => 15:30
22 => 15:45
23 => 16:00
24 => 16:15
25 => 16:30
26 => 16:45
0.2 => crawl across the finish line!

### I can do this. I CAN DO THIS!

With that breakdown, I feel quite confident that I can make it.

I’ll pop into the comments after I’m done and let you know how it went.

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### 2 Responses to Marathon Math – The Math Behind the Houston Marathon

1. YOU DID IT! You finished! (I did some cyberstalking around the Houston Marathon web site!) Congratulations. YOU are a marathoner. NO ONE can take that away from you.

• Bon says:

Thanks, Kevin!

And did you notice I finished just 5 seconds under the 6 hour time limit? #whew

I enjoyed it so much, I’ve already registered for it next year!

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