You have to add your own impedance attribute to the network and set up the "evaluators" correctly to calculate the travel time based on the road lengths and the speed limits.
Here are some documentation pages that might help you out:
- Exercise 1: Creating a network dataset—Help | ArcGIS Desktop
- Understanding network attributes—Help | ArcGIS Desktop
- Types of evaluators used by a network—Help | ArcGIS Desktop
That said, unless you have a compelling reason to create your own network dataset in this manner, you might get better results more quickly by either purchasing a Streetmap Premium network dataset for your area of interest or using Esri's ArcGIS Online routing services. The data quality will likely be better, and it saves you a large amount of time in creating and debugging your own network dataset.