Final answer:
Luke's watch falls behind 4 seconds every day. To determine the number of days since he last set his watch, we can set up and solve an equation.
Step-by-step explanation:
To find out how many days it has been since Luke last set his watch, we need to calculate the number of seconds his watch falls behind each day. Luke sets his watch 3 seconds behind initially, and it falls behind another 4 seconds every day.
Let's use the equation:
Seconds behind = Initial delay + (Number of days - 1) * Additional delay per day
Since his watch is currently 39 seconds behind, we can plug in the values:
39 = 3 + (Number of days - 1) * 4
Subtract 3 from both sides to isolate the variable:
36 = (Number of days - 1) * 4
Divide both sides by 4:
9 = Number of days - 1
Add 1 to both sides:
Number of days = 10
Therefore, it has been 10 days since Luke last set his watch.