I would like to update a time field when another field has been changed.

I would like to update a time field when another field has been changed. For example, I have a status field that is automatically filled with the value "open", but I would like the time field to be filled in with the time that it is set to "Closed". My boss does not want the time to be manually edited by users, as they could set the time to an earlier point in order to make it seem like the calls were closed sooner.