Question

What is the purpose of having Date and Time classes when there is a DateTime class that can handle both?

Answer 1

DateTime is a subclass of Date, so whatever you can do with Date can be done with DateTime. But as tadman and steenslag point out, DateTime is slower. See steenslag’s answer for how much slower it is.

With respect to DateTime vs, Time, I found something here:

Time is a wrapper around Unix-Epoch.
Date (and DateTime) use rational and a "day zero" for storage. So Time is faster but the upper and lower bounds are tied to epoch time (which for 32bit epoch times is something around 1970-2040…while Date (and DateTime) have an almost infinite range but are terribly slow.

In short, DateTime is an all around superstar, and should be preferred in general, but if you want to optimize to the last bit, using Time can improve performance.