1. ## walking the block

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!!

2. the two walkers will be closest when they are directly north/south from each other ... the distance they both travel should sum to 500.

8t + 3t = 500

t = 500/11 sec