Solution:

If he runs up 6 steps, then he needs 67.5 seconds to reach the top.
If he runs up 14 steps, then he needs 47.5 seconds to reach the top.

The 8 additional steps take 20.0 seconds.
Therefore, each step takes 2.5 seconds.

Total steps in escalator = 6 + 67.5 / 2.5 = 33 or Total steps in escalator = 14 + 47.5 / 2.5 = 33.

If Jimmy did not run up any steps at all,
he would reach the top of the escalator in 82.5 seconds (i.e., 33 steps × 2.5 seconds/step).

Alternative Solution through Equations:

Let the total number of steps in the escalator be x.
The escalator moves at a constant speed given by

Speed of escalator = (x − 6)/67.5 = (x − 14)/47.5

The above equation may be solved as follows.

47.5 (x − 6) = 67.5 (x − 14); or
x = (14 × 67.5 − 6 × 47.5) / (67.5 − 47.5) = 33.

Now, Speed of escalator = (33 − 6)/67.5 = (33 − 14)/47.5 = 1/2.5 steps/second.
Time to reach top = Total Steps / Speed = 82.5 seconds.

Food for thought:

Does it matter whether the escalator is moving up or down?