Math and Logic

Not Your Average Average

Kasia is driving on a long stretch of highway with regularly spaced traffic cameras 30 km\SI[per-mode=symbol]{30}{\km} apart. This highway is far too long to be regularly patrolled, so its speed limit of 60 km/h\SI[per-mode=symbol]{60}{\km\per\hour} is enforced by a system which measures the average speed of each car using the time elapsed while traveling between two adjacent cameras.

Halfway between two cameras, Kasia realizes she has been driving at 30 km/h.\SI[per-mode=symbol]{30}{\km\per\hour}. Since she's running late for dinner, she decides to drive as fast as she can (without the traffic cameras noticing she is speeding). How fast can she go in the remaining 15 km\SI[per-mode=symbol]{15}{\km} before the next camera?

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