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## Not Your Average Average

Kasia is driving on a long stretch of highway with regularly spaced traffic cameras $\SI[per-mode=symbol]{30}{\km}$ apart. This highway is far too long to be regularly patrolled, so its speed limit of $\SI[per-mode=symbol]{60}{\km\per\hour}$ 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 $\SI[per-mode=symbol]{30}{\km\per\hour}.$ 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 $\SI[per-mode=symbol]{15}{\km}$ before the next camera?

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