Found this problem from one of my engineering textbooks (introductory chapter). I worked the problem out, found a simple pattern of time error at 9 am and 5 pm each day. I took the first set of days and found a pattern in the time loss, and created a math formula for the pattern based on the Nth day. Cool! I'll give the formula and solution later. I'm curious on if you got this too.

The story is told about the sergeant who stopped at the jewelery store every morning at 9 am and compared and reset his watch with the chronometer in the window. Finally one day the sergeant went into the store and complimented the owner on the accuracy of the chronometer.

"Is it set according to time signals from Arlington?" asked the sergeant?
"No" said the owner, "I set it by the 5 pm cannon fired from the fort. Tell me, Sergeant, why do you stop every day and check your watch?

The sergeant replied, "I'm the gunner at the fort!"

Is the feedback prevalent in this case positive or negative? The jeweler's chronometer loses 2 minutes each 24-hr period and the sergeant's watch loses 3 minutes during each 8 hrs. What is the net time error of the cannon at the fort after 12 days?