In the solution provided, the reduction in the number of steps run from 15
to 7 (=8) causes an increase in time from 17.5s to 37.5s (=20s). 20/8=2.5s
is the time for 1 step to go up on its own.
How can we calculate the total number of steps by 7 + 37.5/2.5? 37.5s is the
total time for the escalator to go up including running 7 out of all steps.
If we use 37.5/2.5, we are assuming every step is taking a constant 2.5s but
how can this be possible when some steps are run up while others are not?
What if we look at it this way?
Running 8 more steps reduces the travel time by 20s. 2.5s will then refers
to the time taken to run up a step.
If he never run at all as compared to running 7 steps, increases the time
travel by 17.5s (7 x 2.5s). Thus total time needed = 37.5s + 17.5s = 55s.
My doubt is: if this is also correct, how can the time taken to run up a
step = time the escalator go up by a step on its own (i.e both 2.5s)???