Automatic task status update when timer has started or Vice a versa

Automatic task status update when timer has started or Vice a versa

We want to start the timer when the task status has changed from Open to RUNNING. In order to keep the track time logs automatic. 
 And when the task status is updated to CLOSED we want to stop the timer. This will give the accurate log of timer.
With current flow we have to go and click on several places to achieve the above.

Also, at the time of task status update. The current time should get noted to someplace. Which can then be used in reporting. Rather than just an activity log. 

The similar feature is there in ZOHO desk , where the timer gets started automatically when the user changes the status of assigned ticket to him/her. The similar is needed here.