Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2016 / Paper 1 / 16 / b / i

Condition throughout on the given arrival time $t$ of A, with $0\le t<r$. A departs at time $r$. B also departs at $r$ exactly when it arrives before that release, so $t+{\tau }_0\le r$, or $0<{\tau }_0\le r-t$. Since ${\tau }_0$ is uniform on an interval of length $R$,The original timeline below shows the three disjoint ranges of ${\tau }_0$. The same idealized simultaneous-release convention as in part (a) is used.