Image copyright Other Image caption Lucy Proctor on the 13-mile run

Can men and women ever compete fairly in a sport like running? Yes, but it requires a little bit of maths know-how.

"What time did you get?" It is the first question runners ask of each other when the race is over. But is it the right question?

You see, distance running is unfair.

Men experience this unfairness as they get older. Ten miles into a half-marathon, older men can only struggle on with growing irritation as younger men - men who would not have stood a chance against them in their prime - sail past.

For women, the feeling of injustice comes as soon as we start racing.

Men have bigger hearts and can take in and move around oxygen much more efficiently than women can. So men can beat us even if we are "better" runners. So is it possible to adjust for age and sex to level the playing field?

To solve this maths problem I challenged my 52-year-old colleague David Lewis to race against me, a 28-year-old woman, in the Great North Run half-marathon.

Then I went in search of a statistician.

FIND OUT MORE Lucy Proctor will be talking about her challenge on BBC Radio 4's More or Less

The programme is broadcast at 1330 BST on Friday, 24 September... ...or listen to it later on the iPlayer

Alan Jones, a retired IBM engineer, is the ultimate number-crunching runner. For decades, he has worked on this very problem for World Masters Athletics (WMA) - the international association for veteran athletes.

Another running enthusiast and statistician, Howard Grubb, has used Alan's figures to create the excellent age-grading calculator now featured on the Runner's World website.

It is painstaking work. Alan plots the best time ever attained at each age and for both sexes over all the commonly run distances, using data from many competitions. He then plots them on a graph - one graph for each distance.

Alan then draws a curve just underneath the times. By comparing points on the curve to the world record time for the 10 kilometres and marathon races, he is able to work out an age-factor.

By multiplying any time at any distance by the correct age-factor and turning the new time into a percentage of the fastest time possible, we get the performance score - how good a given time is compared to the best.

Image copyright bbc

For example, if I get a time of one hour 40 mins, I first turn it into seconds - 6,000. Using Alan's tables, I can see the age-factor for my age of 28 is 1 - because I am too young to yet have one. So I just divide the top possible time for that distance by a woman - 3950 seconds - by 6,000 to see how I compare, and I get a performance score of 65.8%.

As women are only compared with other women, and men with other men, the performance percentage automatically adjusts for sex.

Alan's numbers give us the secret to a fair race. For example: if you compare the best possible time for men and women over a half marathon you get a factor of 0.8995. The age-factor for a 48-year-old man is also 0.8995.

So a young woman (younger than 30) can race against a 48-year-old male happy in the knowledge that it is a fair contest.

"Of course, it is fair anyway," says Alan. "If he runs faster than you, he runs faster than you. That's the nature of a race."

I chose to ignore that bit, as David and I made our way to Newcastle.

So, who won?

Alan's tables throw up an interesting Great North Run fact. Because he uses times for the marathon and 10km races to plot the half-marathon times, he has shown that the current female half-marathon world record set by Lornah Kiplagat in 2007 - one hour, six minutes and 25 seconds - is short of what should be possible.

How did they do? Image copyright Other Half marathon - 13.1 miles

Great North Run 2010 winning time: Haile GebreSelassie 00:59:33 (37-years-old)

Haile's performance score: 101.26%

David's finishing time: 1:40:23

Lucy's finishing time: 1:37:19

David's performance score: 67.86%

Lucy's performance score: 67.65%

His tables show a best possible time of 1:05:39. The fastest time ever run by a woman at half marathon was by our very own Paula Radcliffe, in the Great North Run, in 2003. She achieved 1:05:40- but, sadly, the Great North Run isn't recognised as a world record course.

Using Alan's tables and working backwards, I calculated out that if David and I were both to finish between one hour 30 minutes and one hour 40 minutes, I would have to beat him by at least three-and-a-half minutes just to get an equal percentage score of 68%. By 52, it seems, age is a greater handicap than sex.

In the end I finished exactly three minutes earlier than David. So according to Alan Jones, David beat me by 30 seconds.

But forget fairness. I still crossed the line first.