Is it better run or walk up a hill in a 10 km (6.2 mile ) race?

You should certainly try your best to run at all times. That is, if your level of conditioning allows for it. As another poster mentioned about pace, you will slow down, or if you are an experienced racer, you may only feel as if you are slowing. Even if you aren't able to keep your pace, running slow is still faster than walking! As long as you're putting one foot in front of the other you'll be moving forward. If you can do that a little bit faster by easy running instead of walking you could save yourself a lot of time. For example: Your projected speed would be 10km/h. If you slow to a walking pace of even 7km/h during kilometer 9, you would have to increase your speed to 13km/hr in the last km to compensate. For a beginner or intermediate racer, I would suggest trying to forget that you are on a hill. Push with what effort you can afford and even if your pace does slow, you'll know that you're adding the least amount of extra seconds to your finishing time and that there will be less time to make up in the remaining miles. If you do decide that you need to take a walking break - instead of at a hill, try to time it at the water station. This allows you to at least take full advantage of the stop, and doesn't result in two stops to walk during the race.

um, you shouldnt stop. unless you want to get a stich. if you stop to walk that means your giving up. just run up the hill with your upper body forward, you should feel alrite if you do that. BUT DONT WALK!

Run up the hill. If you walk then you will have to start running again which will make you even more tired. Run slowly if you have to but resist the urge to walk, slowing down and starting is very hard on your heart and lungs.