I hold my ground for as long as possible. She's got to be near to the end of her lunch hour by now - surely her sandwiches are calling. At dangerous risk to my balance, I again glance sideways at the adjoining treadmill to check that my neighbour hasn't surreptitiously upped the game and increased her speed. She catches me looking and the awkward truth dawns - she's being raced, unwittingly, by a colleague. In the office gym. At stake is not just a question of superior fitness levels. I want to win in revenge for that sarcastic comment she made in a meeting last week. The fact that she is paid more than me will cease to matter as long as I finish this session ahead of her, proving that I am more determined, more willing to go to extremes, more steely-eyed than she is - if only on the running machine.
We finish our runs with sweaty smiles and congratulations, of course, displaying no hint of the blatant rivalry that has followed us from boardroom to gym.
When Russian President Vladimir Putin holds fitness sessions with his associates, he has the confidence to be more obvious about the competition involved. In pictures this week taken by the Russian state news agency, Putin is photographed at his summer residence in Sochi, working out with the Prime Minister, Dmitry Medvedev. Dressed in grey tracksuit bottoms and tight fitting T-shirts, Russia's leaders are pictured rattling out pull-ups, lifting weights and working through stretches. In one video of the scene, Putin can even be seen conspicuously pausing his lifting machine to move a lever further down the weight stack, showing off just how heavy a load he can bear.
As a power statement, it is effective if not subtle. But one photo stands out as even more revealing. In it, Medvedev strains at a rowing machine. The President has stopped his own workout to stand behind him, leaning on another machine, watching with the hint of a smile on his face. Can he be thinking anything other than: "I could do that better"? Putin even gives Medvedev a pat on his lower back half way through one pull - encouragement? Sympathy? A comment on his inferior technique?
We cannot know. But anyone who has ever exercised alongside workmates could imagine that Putin's scrutinising of his colleague's technique doesn't stem from a wholly indifferent place. "The only reason I signed up for the JP Morgan Corporate Challenge [a 3.5-mile road race run in seven countries] was to beat the girl I can't stand at work," admits one friend, Natalie, who works for a management consultancy company. "Then we had the office ping-pong tournament, designed for team bonding - it got so competitive that I could immediately see who all the idiots were and decided I never wanted to work with them."
Rivalry can get particularly out of hand when bosses are involved.
"The new fad in our office at the moment is CrossFit," says Hannah Arnold, 28, product manager at IT business management platform Autotask. "It all started with our MD, who's a real alpha male - one of the lads, really fun - training at 6am several times a week. Then our senior manager joined in, and then our sales manager, even though he's only just had a baby. There was such an obvious domino effect - and there's definitely an element of kudos involved." Of 16 of her colleagues who recently signed up for the office Three Peaks walking challenge, she says, "at least a third were newbies to the company, keen to make a mark".
This tactic can backfire, of course, when enthusiasm outweighs fitness capability and the office new recruit is left sprawling in the mud at the back of the Tough Mudder race.
But working out with the people you work next to does have the potential to be less of a bunfight and more of a constructive experience - although we may need to adopt a slightly more American attitude first. In the United States, the indoor cycling class SoulCycle has 47 studios across the country and they have become major networking hotspots. The company even markets itself specifically to corporate firms with the slogan: "Sweatworking is the new networking." The idea is to connect with clients or colleagues in a more challenging environment than the golf course, and a more healthy one than the pub.
In San Francisco, early morning "board meetings" - surfing sessions - with potential business partners are par for the course among chief executives as a way of testing the mettle of potential new recruits. And at Google's headquarters in California, structures that encourage movement - such as an indoor tree house and a volleyball court - are even built into the office architecture.
In the context of America's passion for personal transformation, this all makes sense. But in Europe, we're slowly catching on too. Fitness is now more than just a hobby, it's an integral part of our lifestyles, even a symbol of status. Arriving at the office in trainers is so acceptable it's not even worthy of mention. Tracking your daily step count against your work rival isn't creepy, it's advisable if you want to get ahead. Exercise has even started to invade the office furniture - Italian gym equipment company Technogym has already developed a four-person boardroom table at which bicycle machines replace chairs.
All this work-based fitness is, of course, fraught with protocol issues. Certain ground rules are crucial. "You don't want it to bring out an ugly part of you," says Donna Flagg, a work communication expert. "So if it's competitive, you want to have an ease about losing, not look like a child who can't handle it." What about when you're winning, for example thrashing your boss in a tennis match? It all comes down to assessing your relationship with your senior colleague, she advises. "If you have a boss who is on a power trip, insecure and full of ego, he/she is not going to take well to being shown up by a subordinate. If, on the other hand, you've got an open, secure individual who won't take it personally, then it could be very positive for both parties. Keep in mind that the game he or she is playing may not actually be tennis."
If jogging meetings and yoga class conferences are the future, we certainly need to develop a healthier approach to intra-office exercise. And that means resisting the urge to get one up on Sally from the fashion desk by beating her on the treadmill.
Working out with co-workers - do's and don'ts
• Pay at least half of the attention you'd devote to dressing for the office to dressing for the gym. See-through leggings and stinking 10?year?old trainers don't make for a professional look.
• Retain a modicum of modesty - the stats from your weekend Strava cycle ride are deadly boring to your own family, let alone your co-workers.
• Seek or offer business advice while in a state of undress in the changing rooms. Or ever in the changing rooms.
• Take on more than you're physically capable of in an attempt to impress. You will never live down the shame of needing a piggy back to complete that 10km race.