Assuming that the race started at Anchorage,
Let x = distance of the musher from Nome
Then, 2x = distance of the musher from Anchorage
So, x + 2x = 1049
3x = 1049
x = 349 2/3 miles
2x = 699 1/3 miles
The musher has traveled 699 1/3 miles from Anchorage.