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I want to make travel time contour map which shows the area people can go from an origin (e.g. downtown, airport) within certain time interval. I have a roadway linear shapefile with the information of travel time and some example maps found online, but lack of the idea how to make the map. Thanks for your help! enter image description here

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What level of license do you have - specifically, do you have access to Network Analyst? If so this is a Service Area analysis. – Chris W Apr 17 '14 at 18:44
This can be done for US & Canada (for free)… – Mapperz Apr 17 '14 at 19:52
up vote 3 down vote accepted

If you're using ESRI you need Network Analyst extension in order to build a network dataset, but with Spatial Analyst you should be able to use the Cost Distance tool to produce something along the lines of your desired "contours."

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