Compute probability two arrivals meet within 15 minutes

Probability puzzle

Two people plan to meet, but they arrive independently at a random time within the next 1 hour.

• Person A’s arrival time is uniformly random in $[0, 60]$ minutes.
• Person B’s arrival time is uniformly random in $[0, 60]$ minutes.
• They meet if the absolute difference between their arrival times is at most 15 minutes (i.e., they are both present within a 15-minute window of each other).

Question: What is the probability that they meet?

(Assume arrival times are continuous and independent.)