1) how many lines are geneuinely so choc- a-bloc with trains that this problem is real. You can go train watching on busy lines and sometimes wait for hours without seeing anything at all.
The line doesn't have to be jam-packed for it to be an issue. You just have to have freight and passenger trains in the same general time period. A long-distance train may travel considerable distance without being delayed by freight trains, but it's not going to go the entire route without encountering some congestion. Some lines, though, are quite congested, and plenty of time can be lost weaving trains in and out of each others' way.
2) Just because a train can run at 79mph it doesn't mean it always will. It may be more efficient to leave a passenger train running behind a freight until the next major yard or junction than to initiate an overtaking operation every time one catches up.
If you want a 48-hour long-distance train trip to take 56 hours, then fine. Essentially, we're coming back to the key debate about whether passenger trains should take priority on a line that primarily serves freight. If you don't care about timeliness and cost, then you may very well be fine with having passenger trains run at freight speeds and following freight trains dependent on the flow of traffic. But that has consequences for both revenue (while someone taking a long-distance train end-to-end may not take speed as their most important factor, eventually the train trip will be too long to be practical, plus there are people traveling on LD trains but taking shorter trips, for whom travel time may be more important, then there is the issue of connections that will be missed due to longer schedules, equipment turns and requirements, etc.) and cost (a longer trip means you're paying the crew for longer, and/or requiring more crews such as conductors and engineers).
The theory is that passenger trains should have priority so they can make good time, but that priority comes with a cost to capacity, and that cost is not covered by what Amtrak pays to the railroads (to bring this slightly back onto the topic of the tangent that this thread went on).
As for following the train just to the next yard, yards can be dozens or hundreds of miles apart. Plus, if that yard isn't actually where the freight train is headed, then you still have a delay to that freight train, which could very well add up to more time than if it just held at a control point for the passenger train to cross over. If you take a 10,000-foot freight train and have it enter a yard at restricted speed (which could be as low as 10 mph on certain railroads for yard speed, and even slower if there are switches or other potential obstructions in that yard), you're talking 10-15 minutes just for the train to get into the yard. If you wind up following four freight trains, you could lose an hour just doing that.
Also remember passenger trains often stop in places where freights don't, so that allows the freight time to make headway. I think in the bigger picture it all averages out.
It doesn't. Most passenger stops are maybe 2-3 minutes, and are spaced fairly well apart. A 79 mph passenger train making brief stops mixes fairly well with a 70 mph freight train that isn't stopping. If the freight is going 60 mph or 55 mph, then something is still going to get delayed.
3) Some freight railroads also run fast freights at passenger speeds. So it's not as if the concept of passenger train speeds is totally alien to them or that they wouldn't have to deal with it anway. A smart scheduler might run a passenger train immeditaely in front of or behind such a fast freight and so minimize disruption.
As already noted, freights don't run at passenger speeds, but some can run fairly fast (70 mph). Those are most compatible with passenger trains in mixed traffic, but depending on the railroad, that may not be a significant portion of the traffic.
To the best of my knowledge, there are only three categories of train speeds: Freight, Passenger, and Auto Train. On the CSX mainline, much of it is listed at 59 MPH for freight, 70 MPH for AT and 79 MPH for passenger.
Actually, in most cases, there are only two categories, freight and passenger.
In the Northwest, there's a special "Talgo" category on the Cascades route.
A quick glance at the CSX timetable shows freight speeds are 60 mph max (speeds ending in 9 usually relate to some specific technology requirement for exceeding the next threshold; 50 mph and above for freight or 60 mph and above for passenger require signals, for example, so in unsignalled territory, they would be limited to 49/59 respectively), and 79 mph for passenger.
The Auto Train counts as a passenger train.
However, there are often equipment-specific restrictions that can be more restrictive than the speed on the line. The Auto Tracks, for example, can run at passenger speeds, but cannot exceed 70 mph. The timetable (and any trackside speed signs, if they exist) wouldn't necessarily say anything about this, but the crews on the train have to be aware of any equipment restrictions that further limit their speed.
There are many examples of freight trains that can't do the full freight speed, as well, because of certain equipment types or other conditions (such as braking capability compared to the weight of the train).