Solution:

If he runs up 8 steps, then he needs 39.0 seconds to reach the top.
If he runs up 15 steps, then he needs 28.5 seconds to reach the top.

The 7 additional steps take 10.5 seconds.
Therefore, each step takes 1.5 seconds.

Total steps in escalator = 8 + 39.0 / 1.5 = 34 or Total steps in escalator = 15 + 28.5 / 1.5 = 34.

If Andy did not run up any steps at all,
he would reach the top of the escalator in 51.0 seconds (i.e., 34 steps × 1.5 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 − 8)/39.0 = (x − 15)/28.5

The above equation may be solved as follows.

28.5 (x − 8) = 39.0 (x − 15); or
x = (15 × 39.0 − 8 × 28.5) / (39.0 − 28.5) = 34.

Now, Speed of escalator = (34 − 8)/39.0 = (34 − 15)/28.5 = 1/1.5 steps/second.
Time to reach top = Total Steps / Speed = 51.0 seconds.

Food for thought:

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