Nope, that's the beauty of CTC signal systems (the standard throughout North America today). On all railroads there are what we call blocks. There can only be one train in a block at a time. Throughout most of the country this is achieved with track circuits, which feeds a computer the information. If there is a train in the block another train can only enter the block if there is a good deal of distance between them, but the train entering can only operate at 30 MPH, slow enough that you could stop if the train in front of you stopped you could easily stop. But if there is not enough distance the train will not be allowed to proceed until there is enough distance or the train has exited the block. This is what is most common in North America. Some smaller sections of track use Track Warrant/Form D blocking. This is cheaper, but only one train per block. The Dispatcher will authorize a train to enter a block, another train cannot enter until that train has released the block to the dispatcher.
So to anwer your question, no we did not hit the Tri-Rail. Since he had just entered the block (by about .3 mile) we recieved a stop signal just behind him. When his engine died because of no gas, his Conductor radioed our Engineer, and said they were out of gas. After talking it out, our train got permission to enter the block at a Restricted speed (15 MPH), and couple up to him. Once we coupled up we pushed him down to the next siding past the switch. Train 90 (which was in siding) came out of the siding, we uncoupled, backed up, went in the siding, and passed him. All in all a 1 hour delay.
