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Two weeks from today, thousands of runners will surge across the bridge from Staten Island to Brooklyn at the start of the New York City Marathon. But somewhere along the 26-mile course, many will run out of gas. Runners call it hitting the wall.

One man who'll be running this year's New York Marathon has come up with a formula to help distance runners stay in the race.

NPR's Richard Knox asked him how it works.

RICHARD KNOX: Ben Rapoport is a runner, a very fast runner.

Mr. BEN RAPOPORT (Doctoral Candidate, MIT): I ran this past spring's Boston Marathon in two hours and 55 minutes.

KNOX: In New York next month, he hopes to cut five minutes off that time. Rapoport's a pretty intense guy. He's getting a Ph.D. in electrical engineering at MIT, and he also happens to be a Harvard medical student who plans to be a brain surgeon. So he decided to apply his brain to the problem of hitting the wall, which happened to him five years ago in New York.

Mr. RAPOPORT: Somewhere in the Bronx, I started to feel like I couldn't keep up the pace. It was awful. I couldn't make my legs run any faster, and when I tried, it was very painful.

KNOX: It's called bonking. Rapoport says of the 200,000 Americans who will run marathons this year, four out of 10 will bonk. And for those of you who want to avoid it, Rapoport's figured out a mathematical formula that tells you how. He's just published it in a journal called PLoS Computational Biology. There's a link to his calculator on our website.

We asked a young marathon runner to help us show how the formula works.

Ms. ERIN WYNER (Marathon Runner): I'm Erin Wyner. I'm a runner.

KNOX: Wyner's 29. We met her at a gym at MIT.

Ms. WYNER: I just completed my eighth marathon last week.

KNOX: What was your time?

Ms. WYNER: 3:08:06.

Mr. RAPOPORT: That's an excellent time. Have you ever hit the wall in a marathon?

Ms. WYNER: I have crashed and burned and hit the wall in my first marathon.

KNOX: Rapoport says it's all about carbohydrates.

Mr. RAPOPORT: When an athlete hits the wall, an athlete is essentially running out of carbohydrates in the leg muscles and in the liver. So when you bring the carbohydrate fuel tank to empty, the body's forced, then, to metabolize fat rather than carbohydrate.

KNOX: Fat is a much less efficient fuel. It takes more oxygen to burn, so an athlete has to pump more oxygen to the muscles to keep going. Rapoport's formula will tell Wyner exactly how many carbohydrates she needs to eat before the race to keep from running out. And there's something else his formula will tell her.

Mr. RAPOPORT: We're going to go through a calculation that will determine Erin's fastest theoretical marathon time, given her body's ability to store carbohydrates.

KNOX: First, he needs to estimate Wyner's maximal capacity to use oxygen. The technical term is VO2-max. To some extent, that's something you're born with. And to some extent, you can improve it with training - lots of training.

Mr. RAPOPORT: I'm going to measure your resting heart rate, so you're sitting here, I'm going to clock your pulse.

KNOX: Hers is 63 beats a minute. That means Wyner should have a VO2-max of 45. That's good. It means she's in the top 10 percent of women her age. Next, Rapoport puts Wyner on a treadmill.

Mr. RAPOPORT: So while you're running at 6.1 miles per hour, I'm going to clock your heart rate.

KNOX: A hundred and twenty beats a minute.

Mr. RAPOPORT: OK. So now I need to know one additional piece of data. I need to know how much you weigh.

Ms. WYNER: Around 100.

Mr. RAPOPORT: A hundred pounds. OK, great.

KNOX: Knowing her weight allows him to estimate how many carbs her body can store. Rapoport plugs all the numbers into his computer and...

Mr. RAPOPORT: It seems that you're capable, at full carbohydrate loading, of running a 2:44 marathon.

Ms. WYNER: Wow.

KNOX: That's 24 minutes faster than her best time. It's enough to qualify her for the Olympics.

Ms. WYNER: Wow.

Mr. RAPOPORT: How does that make you feel?

Ms. WYNER: Surprised.

Mr. RAPOPORT: Potentially good.

Ms. WYNER: Potentially good. I may never live up to it, but it's very intriguing.

KNOX: To run that best time, Rapoport tells her, she'll need to stoke up before the race with 1,900 calories worth of carbs. And, of course, she'll also need a lot more training, not to mention that hard-to-quantify quality called grit. Rapoport's formula isn't just for elite athletes. Any long-distance runner can use it.

Mr. RAPOPORT: It's a beautiful problem, because a little bit of math from a dedicated marathon runner can help a lot of people.

KNOX: Richard Knox, NPR News, Boston.

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