Calculating walking time and driving time from dataset coordinates (British National Grid:Eastling&Northling)?

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I am trying to find a way to get the travel time for both walking and driving for my dataset. Using ArcGIS I was able to get the liner/planar line that connects them but I do not know how to get the travel times. After days spent trying, I am switching to a more practical solution in R!

edit: I have a dataset with 2 sets of coordinates, origin and destination, where each point has its own origin (where the journey started) and a destination (where the journey ended). What I want to do is calculate the driving time and the walking time for these points.

Thank you!

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