Here is a quote from "The Elegant Universe" by Brian Greene.
Imagine two countries that have been at war are sitting down to sign a treaty ending hostilities while traveling aboard a train that is moving at a constant velocity. The catch is that neither country's delegate wants to sign the treaty before the other delegate and thus, a simple system is devised to ensure that both delegates sign the peace treaty simultaneously. The solution involves setting a light bulb at the center of a table in such a way that the light bulb is exactly between the delegate from Forwardland (who is facing the direction the train is traveling) and the delegate from Backwardland (who has her back to the direction the train is traveling). When the light bulbs lights up, that is the signal for both delegates to sign the treaty.
This setup is agreeable to all parties on the train and to both security councils in the countries' respective capitals. Once the bulb lights up and the delegates have simultaneously signed the peace treaty, everyone on the train celebrates the cessation of hostilities, but they are perplexed to discover that fighting has broken out anew between the two countries. The reason given is that the delegate from Forwardland was tricked into signing the treaty before the delegate from Backwardland
Why do the delegates see the light at the same time? the forward land delegate IS approaching the light and the backwardland delegate IS moving away from it. so therefor the delegate from forward land SHOUlD see the light first. (because he traveled less distance to see the light.)
SO how come the observers on the platform outside the train see this but the ones ON the train don't??? Since the speed of light IS constant it makes sense that this would be how everybody saw it, on and off the train. I have searched for an answer to my question for about a month now and haven't a found a satisfying one. Please don't use too complex of vocabulary.