Solution: Let the arrival times of Dr. Tide and Dr. Coral be $ x $ and $ y $, respectively, where $ x, y \in [0, 60] $ minutes after 7:00. The condition $ y > x $ defines a triangular region in the $ xy $-plane with area $ \frac60^22 = 1800 $. The favorable region is where $ x < 45 $ and $ y > x $. Integrating over $ x \in [0, 45] $, the area is $ \int_0^45 (60 - x) \, dx = 60 \cdot 45 - \frac45^22 = 2700 - 1012.5 = 1687.5 $. The conditional probability is $ \frac1687.51800 = \frac34 $. - Abu Waleed Tea