Unless Your Car Can Bore Tunnels
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Well, no matter how you go there are mountains in the way, so what you really need is a route that minimizes grades, i.e., the steepness and length of any hill you'll have to climb. The Interstate Highway System is built to specifications that limits steepness to 6%, and usually when things start getting above 4% or so, they have a "truck lane" at the far right for vehicles which are slowed down by the climb. This is not the case for the older U.S. highway system, which has no such restrictions on grades, and in fact often narrows to two lanes in the mountains. There are two all-Interstate options available to you, both of which are on the order of 1250 miles. The first is as you noted: I-15 south to Barstow, cutting across on CA-58 to I-5 and then take that north to Olympia. You will have the climb over the Siskiyou Pass in northern California. The other route, which may look daunting at first, is to take I-15 north past Salt Lake City and then I-84 to Portland. If your car is up to the journey, it should be up to either of these sets of highways.
AZBuck