How to calculate time between 2 geopoints given a route

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I need to write a Android app that will calculate the walking (or driving) time between 2 points, given a route.

I already can calculate the distance between 2 points using Google Maps API2 (parsing JSON output), but it gives me the time considering a default route (the is normally the shortest possible).

I can also draw a route giving several geo-points (using Polylines). But how to calculate the walking/driving time between two points, considering this polyline I've created?

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