Android - How to get estimated drive time from one place to another?

yes you get the time and distance value as well as many like direction details in driving, walking etc mode. all you got from the google direction api service

check our this links

http://code.google.com/apis/maps/documentation/directions/

    Location location1 = new Location("");
    location1.setLatitude(lat);
    location1.setLongitude(long);

    Location location2 = new Location("");
    location2.setLatitude(lat);
    location2.setLongitude(long);

    float distanceInMeters = location1.distanceTo(location2);

EDIT :

    //For example spead is 10 meters per minute.
    int speedIs10MetersPerMinute = 10;
    float estimatedDriveTimeInMinutes = distanceInMeters / speedIs10MetersPerMinute;

Please also see this, if above not works for you:

Calculate distance between two points in google maps V3