Most running races have a strict ban jogging strollers, and with good reason. It's hard enough for runners to maneuver around runners in crowded races, but running around someone pushing a jogging stroller is not only difficult (wasting valuable energy), it can also be unsafe. It's not fair to other runners to make them have to move around you or slow down.
Make it easier on yourself and run the race stroller-free -- you'll definitely run faster. And if you really want to do a race with your little one, look for an event that is stroller-friendly and stay in the back where you won't get in the way of other runners.
Also see: How Parents Can Find Time to Run
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