Solution:

If he runs up 6 steps, then he needs 77.5 seconds to reach the top.
If he runs up 13 steps, then he needs 60.0 seconds to reach the top.

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

Total steps in escalator = 6 + 77.5 / 2.5 = 37 or Total steps in escalator = 13 + 60.0 / 2.5 = 37.

If Graham did not run up any steps at all,
he would reach the top of the escalator in 92.5 seconds (i.e., 37 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)/77.5 = (x − 13)/60.0

The above equation may be solved as follows.

60.0 (x − 6) = 77.5 (x − 13); or
x = (13 × 77.5 − 6 × 60.0) / (77.5 − 60.0) = 37.

Now, Speed of escalator = (37 − 6)/77.5 = (37 − 13)/60.0 = 1/2.5 steps/second.
Time to reach top = Total Steps / Speed = 92.5 seconds.

Food for thought:

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