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I'm trying to use Arcmap 10.1 to find all the areas along a road network (a county roads layer in this case) that are a certain driving distance from a single origin point. In essence, this would be akin to a service area analysis, except there is only a single facility used rather than a whole list.

Applicability: trying to find where a subject could move to within the county (using census block layers) if they want to live no more than, for instance, an hour's drive from work/school/etc.

Any suggestions?

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This is a service area analysis. You are not required to use more than one origin or multiple break values in the service area analysis solver. You can generate a polygon, detailed or not - the only thing to watch (since you mention county) is that any area completely surrounded by a road will be included, which may lead to misleading polygons depending on break values and just how rural the county is. See Check/Uncheck Trim Polygon option in Network Analyst for more info.

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