First, we should find out whats going on before the dog decides to chase the jogger. No need to worry about the dog, as its just sitting there, but we should figure out how far the jogger ran before the dog starts chasing her...
Now, here is whats going on when the dog starts chasing the jogger, 1 second later... Remember the dog is accelerating, and the jogger is running with a constant velocity
When the dog catches the jogger, their positions must be equal at the same time. Unfortunately we don't yet know when that time will be, so we need to express their positions more generally, as functions of some unknown time (t):
Now in order to find when they meet, we need to set 
equal to
, and solve for t:
Now we can use the quadratic equation on to solve for t.
Which yields two possible solutions:
The problem with the quadratic equation is that it requires a person to actually
think about the answers to determine which is the correct one... The negative time
is not what we are looking for, because our conditions only
apply after t=0.
Therefore, 