Meeting when arrivals are uniform on different windows

A student will turn up at a time chosen uniformly between 4:00 and 5:00 PM. Independently, Gabe will turn up at a time chosen uniformly between half past four and five. Whoever arrives first waits at most $10$ minutes for the other and then leaves. What is the probability that they meet?

$\tfrac{11}{36}$. In minutes after 4:00, Gabe is $\text{Unif}(30,60)$ and the student $\text{Unif}(0,60)$; they meet if the times differ by at most $10$. For Gabe's time $g\le50$ the student's window has length $20$, and for $g>50$ it shrinks to $70-g$, so the favourable area is $400+150=550$ out of $1800$.