This equation shows how the accuracy of Colin's watch is related to how long it has been since he last set it:

[tex]1.3d + 18.6 = s[/tex]

The variable [tex]d[/tex] represents the number of days that have passed since Colin last set his watch, and the variable [tex]s[/tex] represents how many seconds behind the watch is.

How many days has it been since Colin last set his watch if the watch is 97.9 seconds behind?

The equation relating the accuracy of Colin's watch to the number of days since he last set it is given by

[tex]$$
1.3d + 18.6 = 97.9,
$$[/tex]

where [tex]$d$[/tex] is the number of days and [tex]$97.9$[/tex] is the number of seconds by which the watch is behind.

Step 1: Subtract the constant term from both sides to isolate the term with [tex]$d$[/tex]:

[tex]$$
1.3d = 97.9 - 18.6.
$$[/tex]

Calculating the right side, we have

[tex]$$
1.3d = 79.3.
$$[/tex]

Step 2: Divide both sides of the equation by [tex]$1.3$[/tex] to solve for [tex]$d$[/tex]:

[tex]$$
d = \frac{79.3}{1.3}.
$$[/tex]

Performing the division gives

[tex]$$
d = 61.
$$[/tex]

Thus, Colin set his watch [tex]$\boxed{61}$[/tex] days ago.