To be a sub-4 marathon finisher, you must complete a sub-2 half marathon.

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Came across this statement in a running group, so I'm curious whether this is true. More formally,

Let $x(t)$ be the runner's distance (in km) at time $t$ and $x$ is a weakly increasing function. Given that $x(4) \geq 42.2$, there must be an interval $[a, a+2]$ with $a \in [0,2]$ such that $x(a+2)-x(a) \geq 21.1$.