two men are on opposite corners of a square block with 500feet sides. If they start to walk at the same time with one man walking east at 8ft per second and the other walking west at 3 ft per second at what time (in seconds) are they the closest?

So the closest they can possibly be is 500 feet and I need to know when that happens.

I set up the problem originally by just saying 8t-3t = 500

but this was wrong and when I started looking at the diagram I saw that the original distance could be determined with the Pythagorean theorem such that: 500^2 + 500^2 = 500,000 so that the distance between them equals approx. 707 feet.

So I am thinking that there may be some way to incorporate the triangle into the proper equation for this problem... but as the men change positions I lose track of how to find the new base of the triangle, I only know that I want the height to be 500 feet.

Does this seem right? Any hints as to how to make this work?

Thanks!!