Alexandra Alter follows a 47-year-old woman out to conquer 548 miles of mountains, snow and exhaustion. Big Sky, Mont. Four days and 263 miles into a backcountry race and Kathy Roche-Wallace isn't even halfway to the finish. She's limping on a big toe that is infected and swollen. She has a purple bruise the size of a grapefruit on her left thigh from a spill down a mountainside. Her sweat smells of vinegar and ammonia, a sign her fuel-starved body has started burning muscle. Ms. Roche-Wallace is 47 years old and has six children. Her oldest, Melissa Hughes, 27, has joined her on this 548-mile race through southwest Montana. It's just past 10 a.m. in late June, but Ms. Roche-Wallace has stopped counting hours or days. She has run 100-mile races and knows that keeping track of time can chip away at one's resolve. "You have to...
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