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On Greyhound, there is a companion fare system where, after the first person, all other persons of the same fare type will get 50% off the full fare. This provides effective comp against cars, resulting in exponential bus growth.
 
You have to think more about gas when driving your own car:

1. The government reimberses 0.55 per mile for business purposes. Depending what you drive, that could be alot or it might not be enough. To dribe round trip 500 miles each way that would cost you about $550. I highly doubt a coach ticket would cost you that much.

2. Even if you are looking at just gas prices, your vehicle probably gets between 15 to 30 miles per gallon depending if you drive an SUV or hybrid. Maybe even less if you drive an old beater pick up. Average price of gas for AZ and CA lets say is $4.00 per gallon. So at those milage rates you end up paying betwenn about $130 to $270 for just gas. This does not include inurance, maintenance (i.e. oil changes, repairs, tires, breaks, etc.), registration, inspections, etc. So how much is it for a round trip ticket? I just found tickets for $85 or $170.
1) That reimbursment is somewhat generous compared to a lot of cars' mileage, and it also includes wear and tear.
The $0.55 per mile is a realistic median cost of owning and driving a car. Add up all the costs sometime over the number of miles driven from the time you buy the car and the time you sell. Most people way underestimate how much driving a car around costs on a per mile basis. But that is a topic for another thread and forum.
Your logic makes perfect sense if I didn't have to own a car. Unfortunately, 98% of us (including me) can't survive without a car. No matter how great Amtrak service is, I will still have to pay for insurance and depreciation and own a car.

For my family of 3 to get from Tucson to LA, its $46 * 3 = 138 (cheapest fare possible). On the other hand, I can fit my whole family in my Malibu, pay $65 for fuel, and be there in six hours instead of ten (and have a car to get around once I arrive). I would prefer to take the train rather than drive... but I refuse to pay double. I'll never take the train unless it saves my family money. How can Amtrak achieve this?
Amtrak may not be less expensive for a group of three... but you aren't counting your car's costs correctly. Those pro-rail foamers at AAA say that a rough metric for an automobile's operating costs is to double fuel consumption. Includes wear and tear on car and tires, insurance components, and (presumably) average operating costs that I'm not thinking of. Does not include amortization (ownership). Also does not include safety (risk of accident) or misbehavior (so, presumes you have never gotten a ticket, and that there are no costs there).

Obviously, this would vary by car. A very well-made car would cost more up front, but require less maintenance. An AMC Gremlin, well.... But, remember, this is a "rough" metric.

If you never do anything for your family that is not the cheapest thing, well, this probably doesn't change your conclusion.
 
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