Not true. Over a set distance the calories you burn running or walking will be almost the same.
NOT TRUE. 3 REASONS (and this has been proven)
(1) When you run, the motion is more inefficient over the same distance, as running involves a forward/vertical motion that is metabollically more expensive than walking, which involves no vertical propulsion
(2) Post metabolic effects
(3) When you exercise, you need to consider not how many calories you burn, but how many NET calories you burn per hour. The concept of NET calories is important.
Let's suppose you were right, and that walking the same distance and running it involved the same many calories. Consider running 5km's (say 20 minutes) or walking it (1 hour), and that this involved 300 calories.
What you need to do is consider how many net calories the exercise burn. At rest, if you were doing sedentary like standing (let's estimate 100 calories per hour, but I have read anywhere from 90-125). That meas the walk actually only increases your calorie expenditure by 200 calories (300-100), because 100 of those calories you would have burnt anyway. In contrast, the 5 km run increase your calorie expenditure by 267 calories, because in the 20 minutes you would have only burnt 23 calories by standing.
When you run, you burn 300 calories during the 20 minutes, and then for the rest of the hour, you are still standing, burning an additional 67 calories. In contrast, this doesn't happen when your walking. Therefore, there is still a significant difference.
In you think about it then, walking actually really only burns about 200 calories net an hour - not very much, kinda a waste of time IMO. Running in contrast, which for someone who is fit burns about 900+ calories per hour, burns therefore 800 net, about 4 times more than walking, and this is even before you consider post metabolic effects
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