You need to stay out of Grizzly country...
http://www.nps.gov/history/history/online_books/yell/vol14-1-2a.htm
"Ernest Thompson Seton, in his "Lives of Game Animals," has the following to say regarding the speed of the grizzly.
"Swift too, is he, in amazing measure for his build. Those who form their idea of a bear's speed from watching a hulking, slouching prisoner, are sure to be amazed at the real thing. For 50 or 100 yards a Grizzly can go faster than any horse, and keep it up indefinitely. It is well known that in the spring of the year, the Indian ponies that have wintered out and are poor, very commonly become the prey of the Grizzly, who can now catch them on the open plain. Townsend tells of a wounded Grizzly that pursued closely a man on horseback for half a mile, snapping at the horse's heels, and apparently would have captured the object of his wrath but for a timely volley from the man's comrades.
"J. M. Mackenzie describes the famous Grizzly, Clubfoot, as able to keep pace with a horse going downhill, but not uphill.
"In view of this, it will be seen how absurd it is for any man to think that he may escape from a Grizzly by simply running.
"Wright says, 'The Grizzly can outrun the Black Bear by nearly half, no man can match him in speed, and it takes a pretty good horse to catch him.'"
--that of course, being why you always should have a partner in grizzly country--you don't need to outrun the bear--you need only to outrun the partner--
I know grizzlies are fast. But I assume they’re slightly slower than mountain lions. Am I wrong?