Baseball diamond word problem

This isn't a homework problem. I'm trying to go through Calculus and Analytic Geometry by Rodin on my own and I'm already stumped. Here's the problem:

A baseball diamond is a square whose sides are 90 feet. Suppose a man runs around the bases at a speed of 20 feet per second, starting from home plate. Express the shortest straight line distance f between this man and home plate as a function of the time t in seconds since he started running. [Hint: Four equations will be needed.]

This should be easy but I just can't do it. :(

If it matters, I am fine with a hint or a number of hints. I'd prefer to find the answer with some help than to be given the answer outright. So far I've written out a table that gives the horizontal distance, the vertical distance, and the sum of the horizontal and vertical distances for given values of t. I'm not sure how to "mod out" the 90 feet, if that makes sense.