Solution:

If he runs up 8 steps, then he needs 67.5 seconds to reach the top.
If he runs up 15 steps, then he needs 50.0 seconds to reach the top.

The 7 additional steps take 17.5 seconds.
Therefore, each step takes 2.5 seconds.

Total steps in escalator = 8 + 67.5 / 2.5 = 35 or Total steps in escalator = 15 + 50.0 / 2.5 = 35.

If Peter did not run up any steps at all,
he would reach the top of the escalator in 87.5 seconds (i.e., 35 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 − 8)/67.5 = (x − 15)/50.0

The above equation may be solved as follows.

50.0 (x − 8) = 67.5 (x − 15); or
x = (15 × 67.5 − 8 × 50.0) / (67.5 − 50.0) = 35.

Now, Speed of escalator = (35 − 8)/67.5 = (35 − 15)/50.0 = 1/2.5 steps/second.
Time to reach top = Total Steps / Speed = 87.5 seconds.

Food for thought:

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