400 miles is a long day when many of those miles will be on toads that twist and turn. While 400 miles is not bad for a day of driving a interstate, but add some 40 MPH curves, and poor gas mileage in the mountains, requiring another stop for gas, and you will not average 50 miles per hour anymore.
The tunnel is very large, it will handle the 18 wheelers that deliver food to the park. You might not like the pass it goes over much though. From what I recall, the tunnel is right next to a water reservoir, and that is why the tunnel was built.
Take your time, enjoy the drive, and stop at a few scenic overlooks. You might not make it that way again for many years.
You can check the elevations by looking at the area on google.maps Then click Terrain. Zoom in or out far enough that you start to get the elevation lines. You can click on one city, say near the interstate, then click on other cities, and the lake you will pass, to get an idea of the elevation changes. You will want to top off the gas tank before getting to close to the park. Fuel trucked in is expensive, and it is even more expensive in the park boundary, where a fuel spill would be extremely expensive, thus very high insurance costs to bring in fuel. .
Have fun on your trip! I prefer the north entrance, it is not as steep, but requires driving on I-90 all the way to Livingston, then south into the park. Not the ideal way to go when your destination is Fishing Bridge.
Fred.
