Katie, if you had altitude problems as low as Salt Lake City, you definitely need to go out several days in advance of your trip. Camp or motel at a lower altitude (one at which you're comfortable) but hike progressively higher each day. This is the "climb high, sleep low" method that is the preferred method of acclimatization. From the link in Lori's post:

Quote:
"Climb High and sleep low." This is the maxim used by climbers. You can climb more than 1,000 feet (305 meters) in a day as long as you come back down and sleep at a lower altitude.

If you begin to show symptoms of moderate altitude illness, don't go higher until symptoms decrease ("Don't go up until symptoms go down")....

Stay properly hydrated. Acclimatization is often accompanied by fluid loss, so you need to drink lots of fluids to remain properly hydrated (at least 3-4 quarts per day). Urine output should be copious and clear....

Eat a high carbohydrate diet (more than 70% of your calories from carbohydrates) while at altitude.

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May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey