How can I sum consecutive rows if a condition is satisfied in R?

I have a dataframe,

     Date_Time ID Activity ID2 Duration
23 2014-12-21 13:07:00    NI       A      OF    69180 secs
36 2014-12-22 09:22:00    TY       A      JU       60 secs
37 2014-12-22 09:23:00    TY       B      JU      420 secs
38 2014-12-22 09:30:00    TY       C      JU      900 secs
45 2014-12-22 10:50:00    TY       B      KJ      300 secs
63 2014-12-22 14:40:00    TY       A      KJ      300 secs

I want to create a conditional statement that will sum consecutive rows of the Duration column if

The Date_Time in the previous row - Date_Time + Duration on that row is < 60

2014-12-22 09:23:00 - (2014-12-22 09:22:00 + 60) < 60

and if both ID and ID 2 are the same in those consecutive rows.

The result should look like this:

 Date_Time ID Activity ID2 Duration Duration_Sum
23 2014-12-21 13:07:00    NI       A      OF    69180 secs    69180 secs
36 2014-12-22 09:22:00    TY       A      JU       60 secs        0 secs
37 2014-12-22 09:23:00    TY       B      JU      420 secs      480 secs
38 2014-12-22 09:30:00    TY       C      JU      900 secs     1380 secs
45 2014-12-22 10:50:00    TY       B      KJ      300 secs        0 secs
63 2014-12-22 14:40:00    TY       A      KJ      300 secs        0 secs

Hope you can give me some help. This is my frist day using R... So if you could also explain your steps it would be great!

Thank you!