Acycle track is 500 metres long. amy completes 10 laps. she travelled at an average speed of 12.5 metres per second. she puts one fast lap completing it in 35 seconds. what was the average speed for the first 9 laps?

The fast lap is irrelevant to the question, because it didn't happen
until after the 9 laps that you're interested in.

To be perfectly technical about it, we don't actually have enough
information to answer the question.  You told us her average speed
for 10 laps, but we don't know anything about how her speed may
have changed during the whole 10 laps.  For all we know, maybe
she took a nap first, and then got up and drove 10 laps at the speed
of 125 metres per second.  That would produce the average speed
of 12.5 metres per second and we would never know it  Why not ?
That's only 280 miles per hour.  Bikes can do that, can't they ?

IF we can assume that Amy maintained a totally steady pace through
the entire 10 laps, then we could say that her average for 9 laps was
also 12.5 metres per second.